$\frac{HS}{H\cap S}$ is a Sylow $p-$subgroup of $\frac{G}{H}$.

Question

Let $H\trianglelefteq G$ and $S$ a Sylow $p-$subgroup of $G$, then

1. $H\cap S$ is a Sylow $p-$subgroup of $H$.

2. $\frac{HS}{H\cap S}$ is a Sylow $p-$subgroup of $\frac{G}{H}$.

I already have the proof of the first statement (with the help of this site). I have questions on the second.