[[Fact about::intermediate subgroup condition]]

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	Uses	Fact about
2-hypernormalized satisfies intermediate subgroup condition	Normality satisfies transfer condition	2-hypernormalized subgroup Intermediate subgroup condition
AEP does not satisfy intermediate subgroup condition		AEP-subgroup Intermediate subgroup condition
Central factor satisfies intermediate subgroup condition		Central factor Intermediate subgroup condition
Characteristicity does not satisfy intermediate subgroup condition		Characteristic subgroup Intermediate subgroup condition
Cocentrality satisfies intermediate subgroup condition		Cocentral subgroup Intermediate subgroup condition
Composition of subgroup property satisfying intermediate subgroup condition with normality equals property in normal closure		Intermediate subgroup condition Composition operator Normal subgroup Normal closure
Conjugate-permutability satisfies intermediate subgroup condition		Conjugate-permutable subgroup Intermediate subgroup condition
Full invariance does not satisfy intermediate subgroup condition		Fully invariant subgroup Intermediate subgroup condition
Hall satisfies intermediate subgroup condition	Index is multiplicative	Hall subgroup Intermediate subgroup condition
Homomorph-containment satisfies intermediate subgroup condition		Homomorph-containing subgroup Intermediate subgroup condition
Intermediate subgroup condition equals upper intersection-closed		Intermediate subgroup condition
Intermediate subgroup condition is right residual-preserved		Intermediate subgroup condition Right residual-preserved subgroup metaproperty
Lattice-complemented does not satisfy intermediate subgroup condition		Lattice-complemented subgroup Intermediate subgroup condition
Left-extensibility-stable implies intermediate subgroup condition		Left-extensibility-stable subgroup property Intermediate subgroup condition
Left-inner implies intermediate subgroup condition	Inner is extensibility-stable Left-extensibility-stable implies intermediate subgroup condition	Left-inner subgroup property Intermediate subgroup condition
Modularity satisfies intermediate subgroup condition		Modular subgroup Intermediate subgroup condition
Normality satisfies intermediate subgroup condition		Normal subgroup Intermediate subgroup condition
Permutably complemented satisfies intermediate subgroup condition		Permutably complemented subgroup Intermediate subgroup condition
Pronormality satisfies intermediate subgroup condition		Pronormal subgroup Intermediate subgroup condition
Subhomomorph-containment satisfies intermediate subgroup condition		Subhomomorph-containing subgroup Intermediate subgroup condition

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