Homomorph-containing subgroup of finite group

Definition
A subgroup of a group is termed a homomorph-containing subgroup of finite group if the whole group is a finite group and the subgroup is a homomorph-containing subgroup of it.

Stronger properties

 * Weaker than::Variety-containing subgroup of finite group
 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup
 * Weaker than::Subgroup of finite cyclic group

Weaker properties

 * Stronger than::Isomorph-free subgroup of finite group
 * Stronger than::Fully invariant subgroup of finite group
 * Stronger than::Characteristic subgroup of finite group
 * Stronger than::Normal subgroup of finite group