  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
$G$.
