Using Moller-Plesset second-order perturbation theory (MP2) for the geometry optimizations, we have examined various structural possibilities for the Si4C cluster. The energies of the MP2-optimized structures have been calculated using singles and doubles coupled cluster (CCSD) theory and the CCSD (T) method. The structure of lowest energy is a C-3V symmetric trigonal pyramid made from four silicons and one carbon atom in a face capping position. Very close in energy (around 5 kcal/mol) lies an isomer with C-2V symmetry, resembling the pyramid of the previous structure but with the carbon atom in an edge capping position this time. Both of these structures are closely related to the Sis ground state structure. Planar and linear structures analogous to C-5 and C-4 lie higher in energy and they are transition states in most of the cases examined. To help future experimental tests of our present results, we have computed, at the MP2-level, the harmonic frequencies, infrared intensities, and isotopic shifts for the two lowest-lying isomers. Dipole moments and Is core electron energy shifts are also given. The building up principle we have recently suggested from a study of the Si3C3 clusters is found to be fully operative for the Si4C cluster.