# Group in which every maximal subgroup is characteristic

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A **group in which every maximal subgroup is characteristic** is a group satisfying the following equivalent conditions:

- Any maximal subgroup is a characteristic subgroup.
- Any maximal subgroup is a maximal characteristic subgroup.

## Relation with other properties

### Stronger properties

### Weaker properties

- Group in which every maximal subgroup is normal
- Nilpotent group for finite groups, because for a finite group, the group is nilpotent if and only if every maximal subgroup is normal.
`Further information: Equivalence of definitions of finite nilpotent group`