Let $H \le G$, when does there exists normal complements.

Question

Let $H \le G$, if $H$ is normal in $G$ and $(|H|, |G/H|) = 1$, then according to the famous Schur-Zassenhaus-Theorem we can find a complement in $G$ for $H$. This need not be normal. Now my question:

Are there any sufficient conditions to guarantee that a complement for $H \le G$ is normal?

Answer 1

Let $K$ be complement of $H$, $H$ normalize $K$ if and only if $K$ is normal in $G$.