Central factor satisfies intermediate subgroup condition

Verbal statement
A central factor of a group is also a central factor in every intermediate subgroup.

Generalizations and other particular cases of the generalizations

 * Left-inner implies intermediate subgroup condition
 * Left-extensibility-stable implies intermediate subgroup condition
 * Normality satisfies intermediate subgroup condition
 * Centrality satisfies intermediate subgroup condition
 * Cocentrality satisfies intermediate subgroup condition

Related metaproperties for central factor

 * Central factor does not satisfy transfer condition
 * Central factor satisfies image condition
 * Central factor is upper join-closed