# Subnormal-to-normal subgroup

From Groupprops

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### 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.

## Relation with other properties

### Stronger properties

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

## Metaproperties

### Intermediate subgroup condition

YES:This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup conditionABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition