# Subgroup metaproperty satisfaction:Lookup

From Groupprops

*This is a lookup page, viz a page describing how to look up a certain type of article*

This page addresses how to answer natural questions like: given a subgroup property and a subgroup metaproperty , does satisfy ? 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?