,"Quick phrase","Defining ingredient"
"2-locally finite group",,"Finite group"
"Central subgroup of finite group",,"Central subgroup,Finite group"
"Characteristic subgroup of finite group",,"Characteristic subgroup,Finite group,Strictly characteristic subgroup,Injective endomorphism-invariant subgroup"
"Finite characteristic subgroup",,"Characteristic subgroup,Finite group"
"Finite elliptic subgroup",,"Elliptic subgroup,Finite group,Finite subgroup"
"Finite fully invariant subgroup",,"Fully invariant subgroup,Finite group"
"Finite injective endomorphism-invariant subgroup",,"Injective endomorphism-invariant subgroup,Finite group"
"Finite isomorph-free subgroup",,"Isomorph-free subgroup,Finite group,Isomorph-containing subgroup"
"Finite normal subgroup",,"Normal subgroup,Finite group"
"Finite solvable group",,"Finite group,Solvable group,Polycyclic group,Composition series,Chief series"
"Finite subgroup",,"Subgroup,Finite group"
"Finite subnormal subgroup",,"Subnormal subgroup,Finite group"
"Fully invariant subgroup of finite group",,"Fully invariant subgroup,Finite group"
"Homocyclic normal subgroup of finite group",,"Homocyclic normal subgroup,Finite group,Homocyclic group"
"Homomorph-containing subgroup of finite group",,"Homomorph-containing subgroup,Finite group"
"Isomorph-free maximal subgroup of finite group",,"Isomorph-free maximal subgroup,Finite group,Isomorph-free subgroup,Isomorph-free subgroup of finite group,Maximal subgroup,Maximal subgroup of finite group,Isomorph-containing subgroup,Prehomomorph-contained subgroup"
"Isomorph-free subgroup of finite group",,"Isomorph-free subgroup,Finite group,Isomorph-containing subgroup"
"Locally finite group",,"Locally operator,Finite group"
"Normal Sylow subgroup",,"Normal subgroup,Sylow subgroup,Finite group,Subnormal subgroup,Characteristic subgroup,Fully invariant subgroup"
"Normal subgroup of finite group",,"Normal subgroup,Finite group"
"Prehomomorph-contained subgroup of finite group",,"Prehomomorph-contained subgroup,Finite group"
"Residually finite group",,"Subgroup of finite index,Normal subgroup of finite index,Profinite completion of a group,Subdirect product,Direct product of finite groups,Profinite topology,Residually operator,Finite group"
"Subgroup of finite group",,"Subgroup,Finite group"
"Subnormal subgroup of finite group",,"Subnormal subgroup,Finite group"
"Variety-containing subgroup of finite group",,"Variety-containing subgroup,Finite group,Subhomomorph-containing subgroup,Subisomorph-containing subgroup"
"Verbal subgroup of finite group",,"Verbal subgroup,Finite group"