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Abstract Studies of isolated central galaxies and their satellites have shown that the spatial distributions of the satellites are distinctly “lopsided” with respect to the locations of the central galaxies. Here we extend this type of analysis to larger systems by analyzing the lopsidedness of 280 massive galaxy clusters in the IllustrisTNG300 Λ Cold Dark Matter simulation. Using a pairwise clustering statistic, we compute the probability that pairs of cluster galaxies are separated by a given polar angle difference, Δϕ, in the plane of the sky. Relative to the location of the central cluster galaxy, we find a statistically significant excess of galaxy pairs that are located on the same side of the cluster. The lopsidedness of the galaxy distribution is most pronounced for large clusters and for pairs of intrinsically red galaxies. The results summarized here were presented at the 243rd meeting of the American Astronomical Society.