The primitive permutation groups of certain degrees

This paper precisely classifies all simple groups with subgroups of index n and all primitive permutation groups of degree n, where n = 2.3(r), 5.3(r) or 10.3(r) for r greater than or equal to 1. As an application, it proves positively Gardiner and Praeger's conjecture in [6] regarding transitive groups with bounded movement.