Let $\displaystyle G $ be a group of order $\displaystyle p^n $ where $\displaystyle p $ is prime, and let $\displaystyle H $ be a proper subgroup of $\displaystyle G $. Prove that $\displaystyle H = N(H) $ where $\displaystyle N(H) $ is the normalizer of $\displaystyle H $.

I have not yet studied theorems on p - groups. All I have done is theorems and concepts of subgroups, cosets and the Lagrange's Theorem. Can this question be solved using these concepts?