# Class two normal subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): group of nilpotence class two

View a complete list of such conjunctions

## Contents

## Definition

A subgroup of a group is termed a **class two normal subgroup** if it is a normal subgroup and is also nilpotent, with nilpotence class at most two.

## Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property normal subgroup | subgroups dissatisfying property group of nilpotency class twoVIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions

## Relation with other properties

### Stronger properties

- Abelian normal subgroup
- Central subgroup
- Critical subgroup
- Class two characteristic subgroup
- Commutator-in-center subgroup
- Aut-abelian normal subgroup