I saw [this question](https://math.stackexchange.com/q/518568/91177). The original questioner asserted that the Lagrange's Theorem is sufficient to solve the problem, but I think that the theorem does just say that the order of $H$ divides the order of $A\_n$, but not say that $H$ is a subgroup of $A\_n$... 

Is my opinion correct? If not, please point out my fault. Thank you in advance.