Dummit&Foote p.143 Let $G$ be a group of order 30. Let $P \in Syl_5(G)$ and let $Q \in Syl_3(G)$. If either $P$ or $Q$ is normal in $G$, then both $P$ and $Q$ are characteristic subgroups of $PQ$. .....
I don't understand the above parts, stuck on it for hours. How can it be derived?