What I am trying to prove: Let $G$ be a finite group and $H$ a subgroup of $G$. Then prove that two $p$-sylow of $H$ are contained in different $p$-sylow of $G$.
My attempt was suppose that they are contained in one $p$-sylow of $G$ and trying with the conjugations of $G$ to get it.
I would appreciate some help Thanks
Hint: Suppose $P\in\operatorname{Syl}_p(G)$. What is $P\cap H$? If $P$ contains $P_1,P_2\in\operatorname{Syl}_p(H)$, what does that tell you?