We have computationally investigated the role of intramolecular vibrational modes in determining nonradiative relaxation pathways of photoexcited electronic states in isolated chlorophyll A (ChlA) molecules. To simulate the excited state relaxation from the initially excited Soret state to the lowest excited state Qy, the approach of nonadiabatic excited state molecular dynamics has been adopted. The intramolecular vibrational energy relaxation and redistribution that accompany the electronic internal conversion process is followed by analyzing the excited state trajectories in terms of the ground state equilibrium normal modes. The time dependence of the normal mode velocities is determined by projecting instantaneous Cartesian velocities onto the normal mode vectors. Our analysis of the time evolution of the average mode energies uncovers that only a small subset of the medium-to-high frequency normal modes actively participate in the electronic relaxation processes. These active modes are characterized by the highest overlap with the nonadiabatic coupling vectors (NACRs) during the electronic transitions. Further statistical analysis of the nonadiabatic transitions reveals that the electronic and vibrational energy relaxation occurs via two distinct pathways with significantly different time scales on which the hopping from Soret to Qx occurs thereby dictating the overall dynamics. Furthermore, the NACRs corresponding to each of the transitions have been consistently found to be predominantly similar to a set of normal modes that vary depending upon the transition and the identified categories. Each pathway exhibits a differential time scale of energy transfer and also a differential set of predominant active modes. Our present analysis can be considered as a general approach allowing identification of a reduced subset of specific vibrational coordinates associated with nonradiative relaxation pathways. Therefore, it represents an adequate prior strategy that can particularly facilitates mixed quantum-classical approaches.