# Fully invariant subgroup of finite group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: fully invariant subgroup with a group property imposed on theambient group: finite group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A subgroup of a group is termed a **fully invariant subgroup of finite group** if the whole group is a finite group and the subgroup is a fully invariant subgroup of it.

## Examples

VIEW: subgroups satisfying this property | subgroups dissatisfying property fully invariant subgroup | subgroups whose group part dissatisfies property finite groupVIEW: Related subgroup property satisfactions | Related subgroup property dissatisfactions