Summary: We show that the ground state of a Bose-Einstein condensate of atoms with hyperfine spin \(f = 2\) can be either spin aligned, condensed into pairs of atoms coupled to \(F = 0\) or condensed into triplets of atoms coupled to \(F = 0\). The complete phase diagram is constructed for \(f = 2\) and the generic properties of the phase diagram are obtained for \(f > 2\).