$H$ is called $s$-permutable in $G$ if it permutes with every Sylow subgroup of $G$.
Let $G$ be a finite group, $H$ be a $s$-permutable subgroup of $G$. if index $|G:H|=p$, where $p$ is an odd prime divisor of $|G|$, (Not necessarily the smallest prime). then $H$ is normal subgroup of $G$.
Any help/answer/hint will be appreciated so much; thank you all..