Subgroup property modifier application chart

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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