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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 subgroupsof $G$. In this article we present an algorithm for the computation of thesubgroup pattern of a cyclic extension of $G$ from the subgroup pattern of $G$.Repeated application of this algorithm yields an algorithm for the computationof the table of marks of a solvable group $G$, along a composition series of$G$.

Computing the Table of Marks of a Cyclic Extension