# Maximal subgroup of a product of groups?

1. Dec 24, 2011

### moont14263

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. Dec 25, 2011

### micromass

Is it true in $\mathbb{Z}_2\times \mathbb{Z}_2$??

3. Dec 25, 2011

### moont14263

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.