If $H \triangleleft G$ and $|G/H|=m$, show that $x^m \in H$ for $\forall x \in G$ 
If $H \triangleleft G$ and $|G/H|=m$, show that $x^m \in H$ for $\forall x \in G$. 

My attempt is: since $|G/H|=\frac{|G|}{|H|}=m$, we have $x^{|G|}=x^{m|H|}=e$, then I stuck here. Can anyone guide me ?

Since $(xH)^m=H$, it follows that $x^mH=H$, and thus that $x^m\in H$. 
