# Semantic search

1-automorphism-invariant subgroup, Characteristic central factor, Characteristic direct factor, Characteristic transitively normal subgroup, Completely distinguished subgroup, Conjugacy-closed characteristic subgroup, Finite direct power-closed characteristic subgroup, Fully invariant subgroup, Image-closed characteristic subgroup, Image-closed fully invariant subgroup, Injective endomorphism-invariant subgroup, Isomorph-containing subgroup, Isomorph-free subgroup, Left-transitively permutable subgroup, Normal Hall subgroup, Power subgroup, Purely definable subgroup, Quasiautomorphism-invariant subgroup, Sub-(isomorph-normal characteristic) subgroup, Sub-homomorph-containing subgroup, Sub-isomorph-free subgroup, Subhomomorph-containing subgroup, Surjective endomorphism-balanced subgroup, Transfer-closed characteristic subgroup, Transfer-closed fully invariant subgroup, Variety-containing subgroup, Verbal subgroup