  We investigate various halo occupation statistics using a large galaxy group
catalogue constructed from the SDSS DR4 with an adaptive halo-based group
finder. The conditional luminosity function (CLF) is measured separately for
all, red and blue galaxies, as well as in terms of central and satellite
galaxies. The CLFs for central and satellite galaxies can be well modelled with
a log-normal distribution and a modified Schechter form, respectively. About
85% of the central galaxies and about 80% of the satellite galaxies in halos
with masses $M_h\ga 10^{14}\msunh$ are red galaxies. These numbers decrease to
50% and 40%, respectively, in halos with $M_h \sim 10^{12}\msunh$. For halos of
a given mass, the distribution of the luminosities of central galaxies, $L_c$,
has a dispersion of about 0.15 dex. The mean luminosity (stellar mass) of the
central galaxies scales with halo mass as $L_c\propto M_h^{0.17}$
($M_{*,c}\propto M_h^{0.22}$) for halos with masses $M\gg 10^{12.5}\msunh$, and
both relations are significantly steeper for less massive halos. We also
measure the luminosity (stellar mass) gap between the first and second
brightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\log
M_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with $M_h \la
10^{14.0}\msunh$, indicate that the luminosities of central galaxies are
clearly distinct from those of their satellites. The fraction of fossil groups,
defined as those groups with $\log L_1 - \log L_2\ge 0.8$, ranges from $\sim
2.5%$ for groups with $M_h\sim 10^{14}\msunh$ to 18-60% for groups with
$M_h\sim 10^{13}\msunh$. Finally, we measure the fraction of satellites, which
changes from $\sim 5.0%$ for galaxies with $\rmag\sim -22.0$ to $\sim40%$ for
galaxies with $\rmag\sim -17.0$. (abridged)
