This page lists all the transitive graphs on up to 31 vertices. The data was prepared by Brendan McKay and Gordon Royle (source). The current extension has been made possible by the work of Alexander Hulpke who has constructed all the transitive groups of degree up to 31.
At this stage the numbers are guaranteed correct only up to 26 vertices. The transitive groups on 24, 27, 28 and 30 vertices have not yet been checked by Hulpke.