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.