Let $p$ be a prime number. If $P$ is a $p$-Sylow subgroup of some finite group $G$, then for every subgroup $H$ of $G$, $H \cap P$ is a $p$-Sylow subgroup of $H$.
Let $p$ be a prime number. If $P$ is a $p$-Sylow subgroup of some finite group $G$, then for every subgroup $H$ of $G$, $H \cap P$ is a $p$-Sylow subgroup of $H$.