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    $\begingroup$ Solvable groups are classical and non-solvable groups were classified by Hering (using the classification of finite simple, which is guess is OK by now). See en.wikipedia.org/wiki/2-transitive_group for reference. $\endgroup$ Commented Jul 18, 2010 at 12:41
  • $\begingroup$ I also want a proof for this classification. Do you know if there exist some simple source explaining it? $\endgroup$ Commented Jul 18, 2010 at 13:06
  • $\begingroup$ I believe Robinson's Group Theory book does the solvable case and, modulo the CFSG, Cameron's "Permutation Groups" does the non-solvable case. I can't check either of these right now, though, so I could be remembering wrong. $\endgroup$ Commented Jul 18, 2010 at 13:45
  • $\begingroup$ This kind of classification isn't in principle neat or simple; eventually it also depends on knowing what the finite simple groups are. Probably the most useful recent textbook source is the 1999 LMS Student Text (Cambridge) Permutation Groups by Peter J. Cameron. $\endgroup$ Commented Jul 18, 2010 at 13:53
  • $\begingroup$ The answers given so far indicate that your "good reference" and "all" may be elusive. $\endgroup$ Commented Jul 18, 2010 at 22:12