Let $D$ be a finite simple group with $H < D$ and $K < D$. Also $[D:H]=q$ and $[D:K]=p$, where $p$, $q$ are primes. Want to show that $p=q$.
I want to come up with a contradiction with one of the subgroups being normal. I just couldn't do it with the given information. Please help!
Thank you!