,"Quick phrase","Defining ingredient"
"Conjugacy-closed Hall subgroup",,"Conjugacy-closed subgroup,Hall subgroup"
"Group in which every proper Hall subgroup is solvable",,"Hall subgroup"
"Hall direct factor",,"Hall subgroup,Direct factor,Central factor"
"Hall retract",,"Hall subgroup,Retract"
"Hall subgroup of normal subgroup",,"Hall subgroup,Normal subgroup"
"Hall-extensible automorphism",,"Hall subgroup"
"Hall-relatively weakly closed subgroup",,"Hall subgroup,Weakly closed subgroup"
"Nilpotent Hall subgroup",,"Hall subgroup,Nilpotent group"
"Normal Hall subgroup",,"Normal subgroup,Hall subgroup,Subnormal subgroup,Characteristic subgroup"
"Order-conjugate Hall subgroup",,"Order-conjugate subgroup,Hall subgroup"
"Order-dominating Hall subgroup",,"Order-dominating subgroup,Hall subgroup"
"Permutably complemented Hall subgroup",,"Permutably complemented subgroup,Hall subgroup"
"Pronormal Hall subgroup",,"Pronormal subgroup,Hall subgroup"
"Sylow subgroup",,"Group of prime power order,Index of a subgroup,Order of a group,Hall subgroup"