Possible Duplicate:
Suppose $H$ is the only subgroup of order $o(H)$ in the finite group $G$. Prove that $H$ is a normal subgroup of $G$.
I have to solve the following problem. It's an exercise from Herstein's Topics in Algebra book.
Suppose $G$ is a finite group and let $H$ be a subgroup of $G$. Suppose that $H$ is the only subgroup of $G$ of order $o(H)$. Then prove that $H$ is normal in $G$.
Any hints?