# Any $p$-order subgroup is normal in a $pk$ group

I'm looking to prove that if $$G$$ is a group of order $$pk$$ where $$p$$ is prime and $$p>k$$, that any subgroup $$K\leq G$$ of order $$p$$ is normal in G.

Does anybody have any hints or tips for proving this? I've tried multiple approaches including induction on $$k$$, and haven't really gotten anywhere.

Consider how your subgroup of order $$p$$ acts on the whole group $$G$$ and what you can infer from the orbit-stabilizer theorem in this case.