If $G=G_1\times G_2$ does it follow that $H\leq G \implies H=H_1\times H_2$ where $H_1\leq G_1$ and $H_2\leq G_2$
If $G_1$ and $G_2$ are finite group and $H\leq G_1\times G_2$ then $H=P_1\times P_2$ with $P_i\leq G_i$?