Summary: The method of multidimensional SUSY quantum mechanics is applied to the investigation of supersymmetrical \(N\)-particle systems on a line for the case of separable centre-of-mass motion. New decomposition of the super-Hamiltonian into block-diagonal form with elementary matrix components is constructed. Matrices of coefficients of these minimal blocks are shown to coincide with matrices of irreducible representations of the permutation group \(S_N\), which correspond to the Young tableaux \((N- M,1^M)\). The connections with known generalizations of \(N\)-particle Calogero and Sutherland models are established.