Fully invariant subgroup of finite group

Definition
A subgroup of a group is termed a fully invariant subgroup of finite group if the whole group is a finite group and the subgroup is a fully invariant subgroup of it.

Stronger properties

 * Weaker than::Homomorph-containing subgroup of finite group
 * Weaker than::Normal Sylow subgroup
 * Weaker than::Normal Hall subgroup

Weaker properties

 * Stronger than::Characteristic subgroup of finite group
 * Stronger than::Normal subgroup of finite group