Order-normal subgroup

Definition
A finite subgroup $$H$$ of a group $$G$$ is termed an order-normal subgroup if every subgroup of $$G$$ having the same order as $$H$$ is a defining ingredient::normal subgroup of $$G$$.

Stronger properties

 * Weaker than::Order-unique subgroup
 * Weaker than::Normal Hall subgroup
 * Weaker than::Normal Sylow subgroup
 * Weaker than::Maximal subgroup of group of prime power order
 * Weaker than::Maximal subgroup of finite nilpotent group

Weaker properties

 * Stronger than::Isomorph-normal subgroup
 * Stronger than::Normal subgroup