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## Main Question or Discussion Point

How do we go about finding the number of elements of a cyclic subgroup that's generated by an element in the main group. For example:

The subgroup Z

I would think this subgroup would be {0,1,5,25} but there's supposed to be 6 elements and not four. Whats going on?

The subgroup Z

_{30}generated by 25.I would think this subgroup would be {0,1,5,25} but there's supposed to be 6 elements and not four. Whats going on?