Exercise 4. This software expresses subgroups of \(U\)-groups as internal direct product of subgroups \(Z_1 \times Z_2 \times \cdots \times Z_t\), where \(|Z_i|\) divides \(|Z_{i -1}|\). You may enter specific elements by adding period between the integers. For example, you can enter the elements in the form as 1.9.16.22.29.53.74.79.81, and also the modules \(n = 91\), the result would be \(Z_3 \times Z_3\).

Please enter the elements together with the modulus \(n\) and click the button, the direct product form of \(Z_n\) will show below.
elements:
\(n\):