# Direct factor is quotient-transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., direct factor) satisfying a subgroup metaproperty (i.e., quotient-transitive subgroup property)

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

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## Statement

Suppose are groups such that is a direct factor of and is a direct factor of the quotient group . Then is a direct factor of .