The nucleation of superconductivity in a superconducting disk with a Co/Pt magnetic triangle was studied. We demonstrate that when the applied magnetic field is parallel to the magnetization of the triangle, the giant vortex state of votticity three splits into three individual Phi(0) vortices, due to a pronounced influence of the C-3 symmetry of the magnetic triangle. As a result of a strong pinning of the three vortices by the triangle, their configuration remains stable in a broad range of applied magnetic, fields. For sufficiently high fields, Phi(0) vortices merge and the nucleation occurs through the giant vortex state. The theoretical analysis of this reentrant behavior at the phase boundary, obtained within the Ginzburg-Landau formalism, is in excellent agreement with the experimental data.