Every group is characteristic in itself

Statement
Suppose $$G$$ is a group. Then, $$G$$, viewed as a subgroup of itself, is a characteristic subgroup, i.e., any automorphism of $$G$$ sends $$G$$ to within itself.

Related facts

 * Every group is normal in itself

Opposite facts
Note that it is possible for a group to have a subgroup isomorphic to itself that is not characteristic in it. Explicitly, consider a group that is an countable direct power of a nontrivial group. This group is not characteristic as a subgroup of its direct product with itself, even though it is isomorphic to that direct product.

Proof
The proof follows by definition: any automorphism of a group must send it to within itself.