Subgroup property modifier application chart

Note that the word "Same" in a table means that the given subgroup property is invariant under application of the given subgroup property modifier.

Subgroup property	Left transiter	Right transiter	Subordination	Intersection-transiter	Intersection-closure	Join-transiter	Join-closure	Potentially operator	Intermediately operator
Normal	Characteristic	Transitively normal	Subnormal	Same	Same	Same	Same	Same	Same
Characteristic	Same	Same	Same	Same	Same	Same	Same	Potentially characteristic	Intermediately characteristic
Fully characteristic	Same	Same	Same	Same	Same	Same	Same	Potentially fully characteristic	Intermediately fully characteristic
Subnormal	Same	Same	Same	Same	Same	?	Subnormal join	Same	Same
Permutable	?	?	subpermutable	?	?	Same	Same	Same	Same
Conjugate-permutable	?	SCAB-subgroup	?	?	?	Same	Same	Same	Same