How we can conclude that $p\nmid \sum_{x\in H}|x^G|$ in a group with some elements of order $2p$?

Question

Let $G$ be a finite group such that has some elements of order $2p$, where $p$ is an odd prime. Let $H$ be the set of all elements of order $2p$ in $G$. We can show $G$ acts on $H$ by conjugation. So $H$ cut to partition by orbits of this action. Hence $H=\bigcup_{x\in H}x^G$, where these conjugacy classes are distinct. It follows that $|H|=\sum_{x\in H}|x^G|$. How we can conclude that $p\nmid(\sum_{x\in H}|x^G|)$?