Subnormal-to-normal subgroup

Symbol-free definition
A subgroup of a group is termed subnormal-to-normal if it is either normal in the whole group, or not subnormal in the whole group.

Every subgroup is subnormal-to-normal iff the group is a T-group.

Stronger properties

 * Intermediately subnormal-to-normal subgroup
 * Pronormal subgroup
 * Weakly pronormal subgroup
 * Contranormal subgroup
 * Abnormal subgroup
 * Weakly abnormal subgroup
 * Paranormal subgroup
 * Polynormal subgroup