# Subhomomorph-containment satisfies intermediate subgroup condition

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., subhomomorph-containing subgroup) satisfying a subgroup metaproperty (i.e., intermediate subgroup condition)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about subhomomorph-containing subgroup |Get facts that use property satisfaction of subhomomorph-containing subgroup | Get facts that use property satisfaction of subhomomorph-containing subgroup|Get more facts about intermediate subgroup condition

## Definition

Suppose are groups such that is a subhomomorph-containing subgroup of . Then, is also a subhomomorph-containing subgroup of .