Computing Subgroups of Bounded Index in a Finite Group
Journal of Symbolic Computation
We describe a practical algorithm for computing representatives of the conjugacy classes of subgroups up to a given index in a finite group. This algorithm has been implemented in Magma, and we present some performance statistics.
Cannon, John J.; Holt, Derek F.; Slattery, Michael; and Steel, Allan K., "Computing Subgroups of Bounded Index in a Finite Group" (2005). Mathematics, Statistics and Computer Science Faculty Research and Publications. 611.