Order-normal subgroup

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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 normal subgroup of $G$.

Relation with other properties

Stronger properties

• Order-unique subgroup
• Normal Hall subgroup
• Normal Sylow subgroup
• Maximal subgroup of group of prime power order
• Maximal subgroup of finite nilpotent group

Weaker properties

• Isomorph-normal subgroup
• Normal subgroup