# Number of nth roots of a subgroup is divisible by order of subgroup

From Groupprops

## Statement

Suppose is a finite group, is a subgroup of , and is a positive integer. Consider the set:

Then, the number of elements of is divisible by the order of .

## Related facts

### Similar facts

- Number of nth roots is a multiple of n
- Number of nth roots of any conjugacy class is a multiple of n