We know that for a cyclic group $G$, if $G=A\oplus B$, then for some subgroups $H$ of $G$. We have $G/H=A/H\oplus B/H.$ But, if we know that for a subgroup $H$ of $G$,  $G/H=A/H\oplus B/H.$ Then what conditions do we need to make  $G=A\oplus B$?