Using a large galaxy group catalogue constructed from the SDSS, we investigate the correlation between various galaxy properties and halo mass. We split the population of galaxies in early types, late types, and intermediate types, based on their colour and specific star formation rate. At fixed luminosity, the early type fraction increases with increasing halo mass. Most importantly, this mass dependence is smooth and persists over the entire mass range probed, without any break or feature at any mass scale. We argue that the previous claim of a characteristic feature on galaxy group scales is an artefact of the environment estimators used. At fixed halo mass, the luminosity dependence of the type fractions is surprisingly weak: galaxy type depends more strongly on halo mass than on luminosity. We also find that the early type fraction decreases with increasing halo-centric radius. Contrary to previous studies, we find that this radial dependence is also present in low mass haloes. The properties of satellite galaxies are strongly correlated with those of their central galaxy. In particular, the early type fraction of satellites is significantly higher in a halo with an early type central galaxy than in a halo of the same mass but with a late type central galaxy. This phenomenon, which we call `galactic conformity', is present in haloes of all masses and for satellites of all luminosities. Finally, the fraction of intermediate type galaxies is always ~20 percent, independent of luminosity, independent of halo mass, independent of halo-centric radius, and independent of whether the galaxy is a central galaxy or a satellite galaxy. We discuss the implications of all these findings for galaxy formation and evolution.