Prove that if G is a finite group and $\displaystyle H\leq G$ whose index is the least prime dividing the order of G, then $\displaystyle H\triangleleft G$.

Proof:

This is all I could come up with-

$\displaystyle |G|=|G:H|\times |H|$, $\displaystyle |G:H|=p$, and let $\displaystyle |H|=m$.

Now, $\displaystyle |G|=pm$ and $\displaystyle p| \ |G|$.

Now what do I do?