  We infer the normalization and the radial and angular distributions of the
number density of satellites of massive galaxies
($\log_{10}[M_{h}^*/M\odot]>10.5$) between redshifts 0.1 and 0.8 as a function
of host stellar mass, redshift, morphology and satellite luminosity. Exploiting
the depth and resolution of the COSMOS HST images, we detect satellites up to
eight magnitudes fainter than the host galaxies and as close as 0.3 (1.4)
arcseconds (kpc). Describing the number density profile of satellite galaxies
to be a projected power law such that $P(R)\propto R^{\rpower}$, we find
$\rpower=-1.1\pm 0.3$. We find no dependency of $\rpower$ on host stellar mass,
redshift, morphology or satellite luminosity. Satellites of early-type hosts
have angular distributions that are more flattened than the host light profile
and are aligned with its major axis. No significant average alignment is
detected for satellites of late-type hosts. The number of satellites within a
fixed magnitude contrast from a host galaxy is dependent on its stellar mass,
with more massive galaxies hosting significantly more satellites. Furthermore,
high-mass late-type hosts have significantly fewer satellites than early-type
galaxies of the same stellar mass, likely a result of environmental
differences. No significant evolution in the number of satellites per host is
detected. The cumulative luminosity function of satellites is qualitatively in
good agreement with that predicted using subhalo abundance matching techniques.
However, there are significant residual discrepancies in the absolute
normalization, suggesting that properties other than the host galaxy luminosity
or stellar mass determine the number of satellites.
