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We investigate various halo occupation statistics using a large galaxy groupcatalogue constructed from the SDSS DR4 with an adaptive halo-based groupfinder. The conditional luminosity function (CLF) is measured separately forall, red and blue galaxies, as well as in terms of central and satellitegalaxies. The CLFs for central and satellite galaxies can be well modelled witha log-normal distribution and a modified Schechter form, respectively. About85% of the central galaxies and about 80% of the satellite galaxies in haloswith masses $M_h\ga 10^{14}\msunh$ are red galaxies. These numbers decrease to50% and 40%, respectively, in halos with $M_h \sim 10^{12}\msunh$. For halos ofa 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 thecentral galaxies scales with halo mass as $L_c\propto M_h^{0.17}$($M_{*,c}\propto M_h^{0.22}$) for halos with masses $M\gg 10^{12.5}\msunh$, andboth relations are significantly steeper for less massive halos. We alsomeasure the luminosity (stellar mass) gap between the first and secondbrightest (most massive) member galaxies, $\log L_1 - \log L_2$ ($\logM_{*,1}-\log M_{*,2}$). These gap statistics, especially in halos with $M_h \la10^{14.0}\msunh$, indicate that the luminosities of central galaxies areclearly 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 $\sim2.5%$ 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, whichchanges from $\sim 5.0%$ for galaxies with $\rmag\sim -22.0$ to $\sim40%$ forgalaxies with $\rmag\sim -17.0$. (abridged)

Galaxy Groups in the SDSS DR4: II. halo occupation statistics