Previous results suggest that there is a correlation between the size of the bulge of a galaxy and the number of its dwarf galaxy satellites. This was found to be inconsistent with the standard model of cosmology based on comparisons to semi-analytical dark-matter-only simulations, where no such correlation was found. In this work, we extend these studies using the volume-complete ELVES dwarf galaxy catalog, which increases the number of systems compared to previous work by a factor of four. For each giant galaxy we compiled the bulge-to-total baryonic mass (B/T) ratio and present it as a function of the number of dwarf galaxies surrounding them within 250 kpc (N-250). For the 29 galaxy systems in the ELVES catalog, we find a linear relation between B/T and N-250, which is consistent with previous data. However, for a given stellar mass of the host galaxy, this relation is mainly driven by the galaxies' morphologies: early-type galaxies have a larger B/T ratio and a larger N-250 than late-type galaxies. By investigating spiral galaxies in TNG100 of the IllustrisTNG suite, we tested whether the inclusion of baryons in the simulations would result in differences from those based on Millennium-II. Contrary to dark-matter-only simulations, we do find a correlation between B/T and N-250, indicating that the standard model of cosmology does predict a correlation. The empirical relation between the number of satellites and the bulge to total stellar mass is therefore not necessarily in tension with Lambda cold dark matter.