Order-normal subgroup of group of prime power order

Definition
A subgroup of a group is termed an order-normal subgroup of group of prime power order if the whole group is a group of prime power order and the subgroup is an order-normal subgroup: every subgroup of the group having the same order as this subgroup is a normal subgroup.

Stronger properties

 * Weaker than::Maximal subgroup of group of prime power order

Weaker properties

 * Stronger than::Isomorph-normal subgroup of group of prime power order
 * Stronger than::Normal subgroup of group of prime power order