# Left-transitively WNSCDIN not implies normal

From Groupprops

This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., left-transitively WNSCDIN-subgroup) neednotsatisfy the second subgroup property (i.e., normal subgroup)

View a complete list of subgroup property non-implications | View a complete list of subgroup property implications

Get more facts about left-transitively WNSCDIN-subgroup|Get more facts about normal subgroup

EXPLORE EXAMPLES YOURSELF: View examples of subgroups satisfying property left-transitively WNSCDIN-subgroup but not normal subgroup|View examples of subgroups satisfying property left-transitively WNSCDIN-subgroup and normal subgroup

## Statement

We can have a group and a left-transitively WNSCDIN-subgroup of that is not normal in .

## Proof

### Example of a subgroup of order two

`Further information: dihedral group:D8`

Let be any group with a non-normal subgroup of order two. Then, is left-transitively WNSCDIN in .

For a concrete example, take to be a dihedral group and to be a subgroup of order two generated by a reflection element.