Plasmonic nanoparticle clusters are widely considered experimentally and numerically. In the clusters consisting of one central particle and N satellite particles, not only the magnetic modes but also the toroidal modes can exist. Here, the eigenmodes of such clusters and the corresponding excitation efficiency under the illumination of a plane wave are studied analytically by using the eigen-decomposition method. The angular dependence of the optical response of these clusters is clearly demonstrated. The behavior of excitation efficiency is dependent on both the value and the parity of N, the number of satellite particles. Our results may provide a guide for the selective excitation of plasmonic modes in the plasmonic nanoparticle clusters.