# Submaximal subgroup

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

This subgroup property is a finitarily tautological subgroup property: when the ambient group is a finite group, the property is satisfied.

View other such subgroup properties

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Definition with symbols

A subgroup of a group is termed **submaximal** if there exists an ascending chain:

where each is a maximal subgroup of .

## Formalisms

### In terms of the subordination operator

This property is obtained by applying the subordination operator to the property: maximal subgroup

View other properties obtained by applying the subordination operator

## Relation with other properties

### Stronger properties

### Weaker properties

## Metaproperties

### Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.ABOUT THIS PROPERTY: View variations of this property that are transitive | View variations of this property that are not transitiveABOUT TRANSITIVITY: View a complete list of transitive subgroup properties|View a complete list of facts related to transitivity of subgroup properties |Read a survey article on proving transitivity