# Cyclic implies every subgroup is characteristic

From Groupprops

## Statement

In a cyclic group, every subgroup is a characteristic subgroup.

## Related facts

### Stronger facts

- Cyclic implies every subgroup is quotient-isomorph-free
- Cyclic implies every subgroup is verbal
- Finite cyclic implies every subgroup is isomorph-free
- Locally cyclic and periodic implies every subgroup is characteristic