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The total luminosity of satellite galaxies around a central galaxy, Lsat, is a powerful metric for probing dark matter haloes. We utilize data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys to explore the relationship between Lsat and galaxy properties for a sample of 117 966 central galaxies with z ≤ 0.15. At fixed stellar mass, we find that every galaxy property we explore correlates with Lsat, suggesting that dark matter haloes can influence them. We quantify these correlations by computing the mutual information between Lsat and secondary properties and explore how this varies as a function of stellar mass and star-formation activity. We find that absolute r-band magnitude correlates more strongly with Lsat than stellar mass across all galaxy populations; and that effective radius, velocity dispersion, and Sérsic index do so as well for star-forming and quiescent galaxies. Lsat is influenced by the mass of the host halo as well as the halo formation history, with younger haloes having higher Lsat. Lsat cannot distinguish between these two effects, but measurements of galaxy large-scale environment can break this degeneracy. For star-forming centrals, Reff, σv, and Sérsic index all correlate with large-scale density, implying that the halo agemore »affects these properties. For quiescent galaxies, all secondary properties are independent of environment, implying that correlations with Lsat are driven only by halo mass. These results are a significant step forward in quantifying the extent of the galaxy–halo connection, and present a new test of galaxy formation models.