For a group G with subgroup H, the (left or right) cosets of H partition G and are equinumerous. Thus, if G is finite, the order of H divides the order of G, and the order of any group element divdes the order of G. The converse is true for finite abelian groups, but is not generally true—for example, the alternating group A₄ has order 12 and no subgroup of order 6.