Hochschild–Serre Spectral Sequence

A first-quadrant spectral sequence relating the cohomology of a group extension 1 → N → G → Q → 1 with coefficients in a G-module M: its E2 page is E2^{p,q} = H^p(Q, H^q(N,M)) and it converges to H^{p+q}(G,M), thus expressing the cohomology of G in terms of the cohomology of the normal subgroup N and the quotient Q.