Two-arc-transitive graphs of odd order -- II

Abstract: It is shown that each subgroup of odd index in an alternating group of degree at least 10 has all insoluble composition factors to be alternating. A classification is then given of 2-arc-transitive graphs of odd order admitting an alternating group or a symmetric group. This is the second of a series of papers aiming towards a classification of 2-arc-transitive graphs of odd order.