We granted the defendant’s application for further appellate review to determine whether a defendant’s conviction of violating of an abuse prevention order, pursuant to G. L. c. 209A, § 7, is a lesser included offense of assault and battery on a person protected by an abuse prevention order, pursuant to G. L. c. 265, § 13A (b) (iii). Because we conclude that a violation of an abuse prevention order that contains a mandate to refrain from abuse is not a lesser included offense of assault and battery on a person protected by an abuse prevention order, and that there was sufficient evidence for the jury to determine that the defendant had committed both offenses, we affirm.
Background. At a trial in 2011, the parties stipulated that an abuse prevention order had issued against the defendant, who had proper notice and knew of the order. The order contained the sole directive that the defendant refrain from abusing the victim.1
Two witnesses, a police officer and the defendant’s neighbor, testified for the Commonwealth as follows. Late in the evening on November 2, 2011, the defendant and the victim engaged in an altercation, and both were injured.2 A neighbor who was outside listened to the altercation for forty-five minutes. She heard the victim screaming, the defendant’s repeated shouts of “you hit me,” “go to bed,” and “shut your mouth,” and the recurring sound of a “fist to skin.” The neighbor saw the defendant push the victim into a rack that held digital video discs (DVDs). The defendant then left the apartment. The neighbor contacted police, who arrived at the defendant’s apartment with the neighbor a few minutes later. They saw the victim; the officer took photographs of her injuries. The apartment was in disarray, with the rack on the floor and items strewn about.
At the close of the Commonwealth’s evidence, the defendant *288moved for a required finding of not guilty based on insufficient evidence. The judge denied the motion. The defendant then testified on his own behalf. His testimony was that the victim had physically attacked him multiple times that night, which required him to defend himself. When the victim, who is “half [his] size,” bit him on the elbow and kicked him in the face, he responded by hitting her with his elbow and throwing her into the DVD rack. At the close of all evidence, the defendant renewed his motion for a required finding of not guilty because of insufficient evidence, which the judge denied.
The jury convicted the defendant of committing assault and battery on a person protected by an abuse prevention order, pursuant to G. L. c. 265, § 13A (b) (iii), and of violating an abuse prevention order, pursuant to G. L. c. 209A, § 7.3 The defendant received a sentence of two and one-half years in a house of correction for the crime of assault and battery on a person protected by an abuse prevention order and a sentence of probation for two years for violation of an abuse prevention order. More than one week later, the defendant again renewed his motion for a required finding of not guilty because, he argued, the charge of violating an abuse prevention order is a lesser included offense of the charge of assault and battery. The judge denied this motion. In a decision issued pursuant to its rule 1:28, the Appeals Court affirmed. Commonwealth v. Torres, 83 Mass. App. Ct. 1126 (2013).
Discussion, a. Duplicative convictions. The defendant argues that the two offenses of G. L. c. 209A, § 7, and G. L. c. 265, § 13A (b) (iii), are duplicative because the elements of violating an abuse prevention order are encompassed by the elements of assault and battery on a person protected by an abuse prevention order and, therefore, his convictions violate his right to be free from double jeopardy under the Fifth Amendment to the United States Constitution and art. 12 of the Massachusetts Declaration of Rights.4 We disagree.
“[A] defendant may properly be punished for two crimes *289arising out of the same course of conduct.” Commonwealth v. Valliere, 437 Mass. 366, 371 (2002), quoting Morey v. Commonwealth, 108 Mass. 433, 434 (1871). “As long as each offense requires proof of an additional element that the other does not, ‘neither crime is a lesser-included offense of the other, and convictions [of] both are deemed to have been authorized by the Legislature and hence not [duplicative].’ ” Commonwealth v. Vick, 454 Mass. 418, 431 (2009), quoting Commonwealth v. Jones, 382 Mass. 387, 393 (1981). “This elements-based approach remains the standard for determining whether multiple convictions stemming from one criminal transaction are duplicative.” Commonwealth v. Vick, supra. “[T]he elements of the crimes charged are considered objectively, abstracted from the facts [of any particular case].” Id., quoting Commonwealth v. Jones, 441 Mass. 73, 76 (2004).
The elements of a lesser included offense are necessarily a subset of the elements of the greater offense. Commonwealth v. Porro, 458 Mass. 526, 534-535 (2010). An offense is a lesser included offense only if one cannot be found guilty of the greater offense without also being guilty of the lesser offense. See Commonwealth v. Suero, 465 Mass. 215, 220 (2013). A conviction pursuant to G. L. c. 265, § 13A (b) (iii), requires evidence that the defendant touched the alleged victim without having any right or excuse for doing so; that the defendant intended to touch the alleged victim; that the touching either was likely to cause serious bodily harm to the alleged victim or was done without consent; that a court had issued an abuse prevention order or judgment pursuant to G. L. c. 209A against the defendant; that the order was in effect at the time of the alleged assault and battery; and that the defendant knew that the order was in effect. G. L. c. 265, § 13A (b) (iii). A conviction pursuant to G. L. c. 209A, § 7, requires proof that a valid abuse prevention order was in effect at the time of the alleged violation; that the defendant knew about the order; and that the defendant violated the order. Edge v. Commonwealth, 451 Mass. 74, 76 (2008).
*290Here, violation of an abuse prevention order is not a lesser included offense of assault and battery on a person protected by an abuse prevention order because, although there is some overlap, each crime has at least one element that the other does not. General Laws c. 265, § 13A (b) (iii), requires the commission of an assault and battery that G. L. c. 209A, § 7, does not require. General Laws c. 209A, § 7, requires proof that the defendant violated the abuse prevention order, an element G. L. c. 265, § 13A (b) (iii), does not require.5 See Morey v. Commonwealth, 108 Mass. at 434. Thus, one can be found guilty of violation of an abuse prevention order without also being guilty of assault and battery on a person protected by an abuse prevention order. See, e.g., Commonwealth v. Bell, 460 Mass. 294, 296 n.4 (2011) (defendant who committed felony-murder, arson, and armed home invasion was also convicted of violating abuse prevention order).
Moreover, as the Appeals Court has noted, “it is possible to violate an abuse prevention order in myriad ways.” Commonwealth v. Housen, 83 Mass. App. Ct. 174, 178 (2013). Although the abuse prevention order in this case prohibited only “abuse,” many such orders include other mandates, such as prohibiting any contact with the plaintiff or requiring the defendant to stay away from the plaintiff and the plaintiff’s home and workplace.6 In those circumstances, a defendant may violate the abuse prevention order without committing an assault and battery against the plaintiff. Even where, as here, the sole condition is to prohibit “abuse,” a defendant may violate the abuse prevention order without touching the plaintiff, such as where the defendant verbally abuses the plaintiff. See, e.g., Commonwealth v. Regil, 82 Mass. App. Ct. 275, 276 (2012) (defendant’s threat to victim violated terms of “no abuse” term in abuse prevention order).
*291The defendant’s reliance on Edge v. Commonwealth, 451 Mass. 74, is unavailing. In that case, the Commonwealth prosecuted the defendant for violation of a restraining order pursuant to G. L. c. 209A, § 7, based on multiple acts committed by the defendant in violation of that order. Id. The defendant was convicted. Thereafter, the Commonwealth sought to indict the defendant on the offense of stalking in violation of an abuse prevention order primarily based on conduct of the defendant that had formed the basis of his prior convictions. Id. Because the Commonwealth “attempted to prosecute the same violations twice,” we concluded that the prosecution of the offense of stalking in violation of G. L. c. 265, § 43 (b), was duplicative of the prosecution for violating an abuse prevention order pursuant to G. L. c. 209A, § 7, and therefore implicated double jeopardy concerns.7 Id. at 78.
We note that our conclusion that the two offenses are separate is further supported by the terms of G. L. c. 265, § 13A, which uses, inter alla, a violation of an abuse prevention order as a factor in determining the severity of the sentence for a conviction of assault and battery.8 The enhanced sentences in the statute demonstrate the Legislature’s intent that assault and battery on a person already protected by an abuse prevention order be considered a separate offense from a violation of an abuse prevention order. Because violation of an abuse prevention order is not a lesser included offense of assault and battery on a person protected by an abuse prevention order, conviction of *292both offenses does not violate principles of double jeopardy.9 See Commonwealth v. Johnson, 406 Mass. 533, 535 (1990).
b. Sufficiency of evidence. The defendant also argues that the judge erred in denying his motions for a required finding of not guilty because there was insufficient evidence to prove he committed assault and battery on a person protected by an abuse prevention order. To sustain a denial of a directed verdict, there must have been “enough evidence that could have satisfied a rational trier of fact of each such element beyond a reasonable doubt.” Commonwealth v. Latimore, 378 Mass. 671, 677-678 (1979). There was no error.
Here, the Commonwealth had the burden to prove that the defendant committed assault and battery and that the defendant did not act in self-defense. Based on the neighbor’s testimony about the victim on the night of the altercation, particularly that she saw bruises “all over” the victim’s face, arms, and chest, and had “never seen anybody beaten so bad in [her] life,” and concerning the length of time of the altercation, as well as the photographic evidence showing the victim’s injuries, there was sufficient evidence (viewed in the light most favorable to the Commonwealth) to permit the jury to infer that the defendant committed assault and battery against a person protected by an abuse prevention order. See id. at 677. Where the defendant stipulated to his knowledge of an abuse prevention order issued against him, the jury reasonably could have found that he also violated the order by abusing the victim in violation of G. L. c. 209A, § 7.
The Commonwealth also had the burden to prove beyond a reasonable doubt that the defendant did not act in self-defense, i.e., that he “did not have reasonable concern for his safety, that he did not use all reasonable means to avoid physical combat, or that the force that was used was greater than necessary in all the circumstances of the case.” Commonwealth v. King, 460 Mass. 80, 83 (2011). Here, even if the jury believed that the *293victim attacked the defendant, there was sufficient evidence to support the jury’s conclusion that the defendant used greater force than necessary to defend himself: the victim’s diminutive size in comparison to the defendant; the witnesses’ descriptions, and contemporaneous photographs, of the victim’s injuries; and testimony that the defendant “threw” or “pushed” the victim into the DVD rack.10
Judgments affirmed.
Denial of renewed motion for required finding of not guilty affirmed.
General Laws c. 209A, § 1, defines “[ajbuse” as “the occurrence of one or more of the following acts between family or household members: (a) attempting to cause or causing physical harm; (b) placing another in fear of imminent serious physical harm; (c) causing another to engage involuntarily in sexual relations by force, threat or duress.”
Four photographs of the defendant’s injuries and four photographs of the victim’s injuries were admitted in evidence.
The Commonwealth entered a nolle prosequi for the charges of assault and battery on a person sixty years of age or older, or a person with a disability, pursuant to G. L. c. 265, § 13K.
As the basis for his assertions, the defendant relies on the elements of the *289two charged crimes as stated in the Criminal Model Jury Instructions for Use in the District Court (Mass. Cont. Legal Educ. 2009), which the judge used to instruct the jury.
We decline to categorize this case as one of the “rare circumstances where the purposes of our lesser included offense jurisprudence are not served by a strict application of the [elements-based] doctrine,” Commonwealth v. Porro, 458 Mass. 526, 532 (2010).
Remedies pursuant to G. L. c. 209A, § 3, include directives that the defendant not contact or abuse the plaintiff, mandates to vacate and remain away from the family household and the plaintiff’s workplace, and the award of temporary custody of minor children to the plaintiff.
In Edge v. Commonwealth, 451 Mass. 74, 77 (2008), we also applied the elements test and concluded that a violation of an abuse prevention order pursuant to G. L. c. 209A, § 7, is a lesser included offense of stalking in violation of an abuse prevention order, pursuant to G. L. c. 265, § 43 (Jb), because “a violation of a [c.] 209A order does not require the proof of any fact other than what is required to prove stalking in violation of (§ 43[b]).”
The punishment for assault and battery, pursuant to G. L. c. 265, § 13A (a), is imprisonment for not more than two and one-half years in a house of correction or a fine of not greater than $1,000. In contrast, the sentence for those who are convicted of committing assault and battery and thereby causing serious injury, or committing assault and battery on a pregnant woman or someone protected by an abuse prevention order, pursuant to G. L. c. 265, § 13A (b), is “imprisonment in the [Sjtate prison for not more than [five] years or in the house of correction for not more than [two and one-half] years, or . . . a fine of not more than $5,000, or . . . both such fine and imprisonment.” G. L. c. 265, § 13A (b) (iii).
The defendant also claims that the Commonwealth did not prove the crime that caused the violation of the abuse protection order. The jury had to weigh the credibility of the witnesses’ testimony and apparently found the Commonwealth’s witnesses to be more credible than the defendant. Based on that testimony, there was ample evidence for conviction of a violation of G. L. c. 265, § 13A (b) (iii).
As to the other two factors in determining self-defense, the jury could also have found that the defendant’s repeated demands that the victim “shut [her] mouth” and “go to sleep,” and the length of time he stayed in the apartment after he alleges the victim hit him, demonstrate an absence of concern for his personal safety. A reasonable jury also could have found that the defendant did not use all means to avoid physical combat because he did not leave the apartment immediately after the altercation began.