We study the spatial distribution of satellite galaxies around isolated primaries using the Sloan Digital Sky Survey (SDSS) spectroscopic and photometric galaxy catalogues. We select isolated primaries from the spectroscopic sample and search for potential satellites in the much deeper photometric sample. For specific luminosity primaries we obtain robust statistical results by stacking as many as ∼50 000 galaxy systems. We find no evidence for any anistropy in the satellite galaxy distribution relative to the major axes of the primaries. We derive accurate projected number density profiles of satellites down to 4 mag fainter than their primaries. We find that the normalized satellite profiles generally have a universal form and can be well fitted by projected NFW profiles. The NFW concentration parameter increases with decreasing satellite luminosity while being independent of the luminosity of the primary except for very bright primaries. The profiles of the faintest satellites show deviations from the NFW form with an excess at small galactocentric projected distances. In addition, we quantify how the radial distribution of satellites depends on the colour of the satellites and on the colour and concentration of their primaries.