The existence of nonergodic ground states is considered as a precursor to a first-order long-range magnetostructural transformation.  Mn₃Ga_0.45Sn_0.55Clies compositionally between two compounds, Mn₃GaC and Mn₃SnC, undergoing first-order magnetic transformation. However, Mn₃Ga_0.45Sn_0.55C, which crystallizes in a single-phase cubic structure, exhibits more than one long-range magnetic transition. Using a combination of magnetization, ac susceptibility, neutron diffraction, and x-ray-absorption fine-structure techniques, it is shown that, although Mn₃Ga_0.45Sn_0.55C exhibits long-range magnetic order, it presents a cluster glassy ground state due to formation of magnetically ordered Ga-rich and Sn-rich clusters. The clusters are big enough to present signatures of long-range magnetic order but are distributed in a way that limits interactions between two clusters of the same type, leading to a frozen magnetic state at low temperatures. The main reason for such a cluster-glass state is the difference in the local structure of Mn atoms that find themselves in Ga-rich and Sn-rich clusters.