Halo-model interpretations of the luminosity dependence of galaxy clustering assume that there is a central galaxy in every sufficiently massive halo, and that this central galaxy is very different from all the others in the halo. The halo-model decomposition makes the remarkable prediction that the mean luminosity of the non-central galaxies in a halo should be almost independent of halo mass – the predicted increase is about 20 per cent while the halo mass increases by a factor of more than 20. In contrast, the luminosity of the central object is predicted to increase approximately linearly with halo mass at low to intermediate masses, and logarithmically at high masses. We show that this weak, almost non-existent mass dependence of the satellites is in excellent agreement with the satellite population in group catalogues constructed by two different collaborations. This is remarkable, because the halo-model prediction was made without ever identifying groups and clusters. The halo model also predicts that the number of satellites in a halo is drawn from a Poisson distribution with mean which depends on halo mass. This, combined with the weak dependence of satellite luminosity on halo mass, suggests that the Scott effect, such that the luminosities of very bright galaxies are merely the statistically extreme values of a general luminosity distribution, may better apply to the most luminous satellite galaxy in a halo than to brightest cluster galaxies (BCGs). If galaxies are identified with dark halo substructure at the present time, then central galaxies should be about four times more massive than satellite galaxies of the same luminosity, whereas the differences between the stellar mass-to-light ratios should be smaller. Therefore, a comparison of the weak-lensing signal from central and satellite galaxies of the same luminosity should provide useful constraints on these models. We also show how the halo model may be used to constrain the stellar mass associated with intracluster light (ICL): the mass fraction in the ICL is expected to increase with increasing halo mass.