Hi I have this problem, and I cant seem to get it. It is not for a grade just for study practice. Let me know if you can do it. Thanks...

Let G be a group, |G|=$\displaystyle p^{t}m $ for a p a prime and (p,m) =1 and H $\displaystyle \le$ G with |H|=$\displaystyle p^{t}$. If K $\displaystyle \le$ G with |K|=$\displaystyle p^{s}$ and HK = KH, then show K$\displaystyle \le$ H.

Need to show K is a subgroup of H. Thanks again.