Maximal subgroup of finite nilpotent group

This article describes a property that arises as the conjunction of a subgroup property: maximal subgroup with a group property imposed on the ambient group: finite nilpotent group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A maximal subgroup in finite nilpotent group is the following equivalent things:

• A maximal subgroup of a finite nilpotent group.
• A maximal normal subgroup of a finite nilpotent group.
• A subgroup of prime index of a finite nilpotent group.

Relation with other properties

Stronger properties

• Characteristic maximal subgroup of finite nilpotent group
• Maximal subgroup of group of prime power order

Weaker properties

• Maximal subgroup of nilpotent group
• Maximal normal subgroup
• Normal subgroup of prime index
• Maximal subgroup
• Normal subgroup
• Order-normal subgroup
• Isomorph-normal subgroup