Let $\displaystyle G$ be a finite group, and let $\displaystyle n$ be a divisor of $\displaystyle |G|$. Show that if $\displaystyle H$ is the only subgroup of $\displaystyle G$ of order $\displaystyle n$, then $\displaystyle H$ must be normal in $\displaystyle G$.

I'm not really sure what to do with this. It's been a while since I worked with cyclic groups or Lagrange's theorem, and so I may be forgetting some essential tricks.

Any help would be much appreciated!