The group Z modulo 30 is a cyclic group of order 30. The composition factors of Z modulo 30 are Z_2, Z_3, and Z_5.
To find the number of composition series, we need to consider the possible refinements of each composition factor. For example, Z_2 has only one refinement, Z_2 itself. Z_3 has two refinements, Z_3 and Z_1. Z_5 has three refinements, Z_5, Z_1, and Z_5 x Z_1.
Therefore, the total number of composition series of Z modulo 30 is 1 * 2 * 3 = 6.