If G is solvable, and H is a subgroup of G, then H is solvable.Rotman (1995), If G is solvable, and there is a homomorphism from G onto H, then H is solvable; equivalently (by the first isomorphism theorem), if G is solvable, and N is a normal subgroup of G, then G/N is solvable.Rotman (1995), The previous properties can be expanded into the following "three for the price of two" property: G is solvable if and only if both N and G/N are solvable. In particular, if G and H are solvable, the direct product G × H is solvable.
If G is solvable, and H is a subgroup of G, then H is solvable.Rotman (1995), If G is solvable, and there is a homomorp,hism from G onto H, then H is solvable; equivalently (by the first isomorphism theorem), if G is solvable and N is a normal subgroup of G, then G/N is solvable.Rotman (1995), The previous properties can be expanded into the following "three for the price ,of two" property: G is solvable if and only if both N and G/N are solvable. In particular, if G and H are solvable the direct product G × H is solvable.