Let G be a finite group, $H \triangleleft G$ be a normal subgroup and $S$ be a Sylow subgroup of $G$. Show that $H \cap S$ is a Sylow subgroup of $H$.
I'm not too sure where to start here. Assuming that $S$ is a Sylow $p$-subgroup of order $p^n$, I would need to show that $H\cap S$ also has order $p^n$. Then I'm stuck.