# Group in which every maximal subgroup is normal

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

This is a variation of nilpotence|Find other variations of nilpotence | Read a survey article on varying nilpotence

## Definition

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

- Any maximal subgroup (i.e. any proper subgroup not contained in any other proper subgroup) is a normal subgroup
- Any maximal subgroup is a maximal normal subgroup
- There does not exist any maximal subgroup that is contranormal
- There does not exist any maximal subgroup that is self-normalizing