Galaxies that fall into clusters as a part of the same infall halo can retain correlations due to their shared origin. N-body simulations are used to study properties of such galaxy subgroups within clusters, including their richnesses and prevalence. The sizes, densities and velocity dispersions of all subgroups with ≥8 galaxies are found and compared to those of the host clusters. The largest galaxy subgroup provides a preferred direction in the cluster and is compared to other preferred directions in the cluster. Scatter in cluster mass measurements (via five observables), along ∼96 lines of sight, is compared to the relation of the line of sight to this preferred direction: scatter in cluster velocity dispersion measurements show the strongest correlation. The Dressler–Shectman test is an observational method to detect cluster substructure. This test is applied to the cluster sample to see whether the substructure it identifies is related to these subgroups. The results for any specific line of sight seem noisy; however, clusters with large subgroups tend to have a higher fraction of lines of sight where the test detects substructure.