Let $G$ be a finite group. $ H,K \leq G $ and $ K \lhd G $.
$G:H$ and $|K|$ are coprime. Show that $K \leq H $
I started like this:
$G:H = (G:KH)(KH:H)$
Therefore, both $(G:KH)$ and $(KH:H)$ are coprime to $|K|$, but have no idea how to continue. Any clues?