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Maximal subgroup of a product of groups?

  1. Dec 24, 2011 #1
    Let G and H be finite groups. The maximal subgroups of GxH are of the form GxM where M is maximal subgroup of H or NxG where N is a maximal subgroup of G. Is this true?
  2. jcsd
  3. Dec 25, 2011 #2
    Is it true in [itex]\mathbb{Z}_2\times \mathbb{Z}_2[/itex]??
  4. Dec 25, 2011 #3
    not true as {(0,0),(1,1)} is a maximal subgroup of Z_2xZ_2 which is not of that form.
    Thank you very much.
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