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I have studied simple groups of order $60$ and $168$. Specifically, I learned two things below:

  1. All simple group of order $60$ are isomorphic to each other.

  2. All simple group of order $168$ are isomorphic to each other.

Natural question arises from these facts. For a given order, are simple groups isomorphic? Thank you in advance.

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    In addition to the duplicate, check out http://math.stackexchange.com/questions/413021/are-there-any-distinct-finite-simple-groups-with-the-same-order and http://math.stackexchange.com/questions/508734/are-two-finite-groups-of-the-same-order-always-isomorphic and the links to mathoverflow in those questions. – Chris Culter May 30 '16 at 01:45
  • I only know the fact that every simple group of order 60 is isomorphic to $A_5$ – GAVD May 30 '16 at 01:45

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