  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.
