Question:Normal subgroup characteristic subgroup relation

Q: Could you clarify the relationship between normal subgroups and characteristic subgroups?

A: Characteristic means invariant under all automorphisms, normal means invariant under inner automorphisms. Characteristic implies normal, normal not implies characteristic, and characteristic of normal implies normal. See more at characteristic versus normal.

Advanced: Question:Normal subgroup characteristic subgroup invariance confusion.

Wiki surf tip: For these kinds of questions, you can usually find answers in the wiki's main content as follows. Go to either of the pages, and look at the "Relation with other properties" section and search for the other page within that. For instance, try looking for "characteristic subgroup" inside the section Normal subgroup or "normal subgroup" in the section Characteristic subgroup. Here, you will find links to the above pages, just as in the question answer, but in a more organized format. You can also use your browser's "find within this page" functionality if available.

See also: Question:Normal subgroup characteristic subgroup invariance confusion and Question:Normal subgroup characteristic in bigger group.