# Semantic search

Characteristic direct factor, Characteristic transitively normal subgroup, Conjugacy-closed characteristic subgroup, Fully invariant subgroup, Homomorph-containing subgroup, Image-closed characteristic subgroup, Image-closed fully invariant subgroup, Injective endomorphism-invariant subgroup, Injective endomorphism-quotient-balanced subgroup, Isomorph-containing subgroup, Left-transitively permutable subgroup, Marginal subgroup, Normal subgroup having no nontrivial homomorphism to its quotient group, Power subgroup, Purely definable subgroup, Strictly characteristic subgroup, Sub-homomorph-containing subgroup, Surjective endomorphism-balanced subgroup, Transfer-closed fully invariant subgroup