Let $\displaystyle G$ be a finite group and $\displaystyle p$ be a prime.

Prove that if $\displaystyle Q \in Syl_p(G)$ and $\displaystyle H $ is a subgroup of $\displaystyle G$ containing $\displaystyle Q$ then $\displaystyle Q \in Syl_p(H) $.

$\displaystyle Syl_p(G)$ is the set of Sylow p-subgroups of G.