Subgroup metaproperty satisfaction:Lookup

This page addresses how to answer natural questions like: given a subgroup property $$p$$ and a subgroup metaproperty $$q$$, does $$p$$ satisfy $$q$$? While this may look like an abstract formulation, a number of concrete questions can be cast in this language and then solved by hunting through the wiki.

Some examples:


 * Is every normal subgroup of a normal subgroup normal? In property and metaproperty terms: is normality a transitive subgroup property?
 * Is an intersection of permutable subgroups again a permutable subgroup? In property and metaproperty terms: is permutability an intersection-closed subgroup property?
 * Is a contranormal subgroup of a group also contranormal in every intermediate subgroup? In property and metaproperty terms: does the property of being a contranormal subgroup satisfy the intermediate subgroup condition?