Computing the table of marks of a cyclic extension

The subgroup pattern of a finite groups G is the table of marks of G together with a list of representatives of the conjugacy classes of subgroups of G. In this article we present an algorithm for the computation of the subgroup pattern of a cyclic extension of G from the subgroup pattern of G. Repeated application of this algorithm yields an algorithm for the computation of the table of marks of a solvable group G, along a composition series of G.