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Homework Help: Finding sylow subgroups

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Write down all Sylow subgroups of A5 (alternating group). I have them for order 3 and order 5 subgroups, but am not sure about order 4 subgroups.

    2. Relevant equations
    Sylow Theorems etc

    3. The attempt at a solution
    I know the # of 4-subgroups is congruent to 1mod2 (though that's not helpful), and a factor of 60/4=15, from Sylow Thm 3. So it's 1,3,5, or 15. I've found 5 of the form {(ab)(cd), (ac)(bd),(ad)(bc),identity}. If there are more I can't find them, and if that's it how do I show that?
  2. jcsd
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