On Hall subgroups of finite groups

Let $G$ be a finite group and $H$ a subgroup of $G$. Then $H$ is said to be $\tau$-quasinormal in $G$ if $H$ permutes with all Sylow subgroups $\mathcal{Q}$ of $G$ such that $(|H|, |\mathcal{Q}|)=1$ and $(|H|, |\mathcal{Q}^G|)\ne1$. A generalization of Schur–Zassenhaus Theorem in terms of $\tau$-quasinormal subgroups is obtained.