Subgroups of cyclic groups

Every subgroup of a cyclic group is cyclic, and if finite, its order divides its parent's

In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of n, and there is exactly one subgroup for each divisor. This result has been called the fundamental theorem of cyclic groups.

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