  We study satellite galaxy abundances in SDSS by counting photometric galaxies
around isolated bright primaries. We present results as a function of the
luminosity, stellar mass and colour of the satellites, and of the stellar mass
and colour of the primaries. For massive primaries the luminosity and stellar
mass functions of satellites are similar in shape to those of field galaxies,
but for lower mass primaries they are significantly steeper. The steepening is
particularly marked for the stellar mass function. Satellite abundance
increases strongly with primary stellar mass, approximately in proportion to
expected dark halo mass. Massive red primaries have up to a factor of 2 more
satellites than blue ones of the same stellar mass. Satellite galaxies are
systematically redder than field galaxies of the same stellar mass. Satellites
are also systematically redder around more massive primaries. At fixed primary
mass, they are redder around red primaries. We select similarly isolated
galaxies from mock catalogues based on the simulations of Guo et al.(2011) and
analyze them in parallel with the SDSS data. The simulation reproduces all the
above trends qualitatively, except for the steepening of the satellite
luminosity and stellar mass functions. Model satellites, however, are
systematically redder than in the SDSS, particularly at low mass and around
low-mass primaries. Simulated haloes of a given mass have satellite abundances
that are independent of central galaxy colour, but red centrals tend to have
lower stellar masses, reflecting earlier quenching of their star formation by
feedback. This explains the correlation between satellite abundance and primary
colour in the simulation. The correlation between satellite colour and primary
colour arises because red centrals live in haloes which are more massive, older
and more gas-rich, so that satellite quenching is more efficient.
