In this work we present a systematic theoretical study of neutral and positively charged hydrogenated carbon clusters (CnHmq+ with n = 1-5, m = 1-4, and q = 0-3). A large number of isomers and spin states (1490 in total) was investigated. For all of them, we optimized the geometry and computed the vibrational frequencies at the B3LYP/6-311++G(3df,2dp) level of theory; more accurate values of the electronic energy were obtained at the CCSD(T)/6-311++G(3df,2dp) level over the geometry previously obtained. From these simulations we evaluated several properties such as relative energies between isomers, adiabatic and vertical ionization potentials, and dissociation energies of several fragmentation channels. A new analysis technique is proposed to evaluate a large number of fragmentation channels in a wide energy range.