I'm stuck on this problem that I've found in Isaacs' Finite Group Theory. I've tried thinking about it for a while but didn't came up with a solution, so I'm asking for some hints or even for a full solution if you wish, everything is welcomed since I don't see any way to follow.
The problem is the following.
Let $G$ be a finite group and $P\in \text{Syl}_p(H)$, where $H\subseteq G$, meaning that $P$ is a Sylow $p$ group in $H$. Let $N_G(P)$ be the normalizer of $P$ in $G$, and let $N_G(P)\subseteq H$. Then show that $p\nmid|G:H|.$