Martin Hermoso pleaded guilty of being found illegally present in the country after having been previously deported for committing an aggravated felony in violation of 8 U.S.C. § 1326(a) and (b)(2). He appeals the sentence, and we affirm.

I.

The district court adopted the presen-tence report (“PSR”), which noted that, under 8 U.S.C. § 1326(b)(2), the conviction carried a maximum term of 20 years. The PSR correctly calculated that Hermoso’s sentencing guideline range was 41-51 months, but the district court gave 40 months. Hermoso argues that the district court erroneously convicted him of being illegally present after having committed an aggravated felony under 8 U.S.C. § 1326(b)(2), because his six-month Ohio conviction of gross sexual imposition does not qualify as an aggravated felony under the statute. Instead, Hermoso argues, he should have been convicted under subsection (b)(1) of that statute, a different penalty provision for the same crime. Because Hermoso did not raise this objection in the district court, our review is for plain error. United States v. Delgado, 672 F.3d 320, 328 (5th Cir. 2012) (en banc).

II.

As the government concedes, Hermoso’s conviction under Ohio Rev.Code § 2907.05(A)(1) does not qualify as an aggravated felony for purposes of 8 U.S.C. § 1326(b)(2), because 8 U.S.C. § 1101(a)(43)(F) defines an “aggravated felony,” as relevant to this case, as a crime of violence for which the term of imprisonment is at least one year, whereas Hermo-so’s conviction of gross sexual imposition *972 carried a term of only six months. Nor does Hermoso’s conviction qualify as an aggravated felony under 8 U.S.C. § 1101(a)(43)(A), because the Ohio offense cannot be categorically defined as “murder, rape, or sexual abuse of a minor.” The Ohio Code § 2907.05(A)(1) criminalizes “sexual contact with another” where “[t]he offender purposely compels the other person ... to submit by force or threat of force.” The Ohio Code defines “sexual contact” as “touching of an erogenous zone of another, including without limitation the thigh, genitals, buttock, pubic region, or, if the person is a female, a breast, for the purpose of sexually arousing or gratifying either person.” Ohio Rev.Code § 2907.01(B). Thus, the statutory provision under which Hermoso was convicted cannot be said categorically to be “rape” or “sexual abuse of a minor.” 1

Accordingly, Hermoso should have been convicted under 8 U.S.C. § 1326(b)(1), which criminalizes being unlawfully present after having committed a “felony (other than an aggravated felony),” rather than under § 1326(b)(2). Subsection (b)(1) imposes a maximum sentence of 10 years, and subsection (b)(2) imposes a maximum of 20 years. Nevertheless, the guidelines calculation in the PSR and accepted by the district court — 41-51 months — remains unchanged, and the below-guideline sentence of 40 months is well below the 10-year maximum penalty under the correct statutory provision. Thus, although Hermoso has shown clear and obvious error, he correctly concedes that the error likely did not affect his sentence and thereby his substantial rights, so this issue fails on the third prong of plain error review. 2

Despite acknowledging that resentenc-ing is inappropriate, Hermoso asks us to remand for reformation of the judgment to reflect conviction of the correct crime, noting that being convicted under subsection (b)(2) rather than (b)(1) carries a greater stigma and possibility of greater future punishment if convicted of another crime. 3 Even on plain-error review, we have corrected such errors in the judgment, either by directing the district court to do so on remand 4 or by amending the judgment ourselves. 5 The parties dispute which course we should take. By statute this court can “affirm, modify, vacate, set aside *973 or reverse any judgment, decree, or order of a court lawfully brought before it for review, and may remand the cause and direct the entry of such appropriate judgment, decree, or order, or require such further proceedings to be had as may be just under the circumstances.” 28 U.S.C. § 2106. The best reading of the statute confers discretion either to reform the judgment or to remand for the district to do so.

We choose the former. The judgment of sentence is AFFIRMED as modified to reflect a conviction under 8 U.S.C. § 1326(b)(1).