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This simulation study examines the performance of fit indices commonly used by applied researchers interested in latent class clustering (LCC) or finite mixture models. The goal of LCC is to classify subjects from a large heterogeneous set of cases into homogeneous subgroups when the number of subgroups is unknown a priori. Despite the advantages of LCC over the traditional clustering, model selection aided by fit indices remains a significant challenge to researchers. Conditions for the simulation study were selected to mirror conditions found in applied educational and psychological research. The accuracy with which common fit indices identify the true LCC model is examined while varying indicator type (i.e., continuous and categorical), sample sizes, class prevalence, and class enumeration.