# Complete characteristic subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): complete group

View a complete list of such conjunctions

## Definition

A subgroup of a group is termed a **complete characteristic subgroup** or **complete characteristic direct factor** if it satisfies the following equivalent conditions:

- It is complete as a group and is a characteristic subgroup of the whole group.
- It is complete as a group and is a characteristic direct factor of the whole group.