Exercise 1. This software determines the cyclic subgroups of \(U(n) (n < 100)\). Run the program for \(n\) = 12, 15 and 30. Compare the order of the subgroups with the order of the group itself. What arithmetic relationship do these integers have?
Please enter \(n\) and click the button, subgroups of \(U(n)\) will show below.