# Characteristic subgroup of direct factor

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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: characteristic subgroup and direct factor
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## Definition

### Symbol-free definition

A subgroup of a group is said to be a characteristic subgroup of direct factor if it occurs as a characteristic subgroup of a direct factor of the whole group.

### Definition with symbols

A subgroup $H$ of a group $G$ is said to be a characteristic subgroup of direct factor if there are subgroups $K,L$ such that $H$ is characteristic in $K$, and $K \times L = G$.