For the latter three, here is the integer-coefficients (apply Kunneth formula to get your mod-2 coefficients: http://mathoverflow.net/questions/75389/group-cohomology-of-compact-lie-group-with-integer-coeffient As for the first: $H^i(\mathbb{Z}_n)$ is $\mathbb{Z}_n$ for $i$ even, and zero otherwise. Again, apply Kunneth formula for $\mathbb{Z}_2$-coefficients.