There is a close correspondence between the set of subgroups of a finite group G and the set of inequivalent transitive permutation representations of G . For many purposes the latter is as useful as the former and more easily calculated. The present paper describes a program which computes a complete set of transitive permutation representations of G (specified by their values on a fixed set of generators of G ) whenever a single faithful permutation representation of G is supplied.

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Conference 2nd ACM Symposium on Symbolic and Algebraic Manipulation, SYMSAC 1971
Citation
Dixon, J.D. (1971). Permutation representations and the subgroup lattice. In Proceedings of the 2nd ACM Symposium on Symbolic and Algebraic Manipulation, SYMSAC 1971 (pp. 159–161).