"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"