We investigate various galaxy occupation statistics of dark matter halos using a large galaxy group catalogue constructed from the Sloan Digital Sky Survey Data Release 4 ( SDSS DR4 ) with an adaptive halo-based group finder . The conditional luminosity function ( CLF ) , which describes the luminosity distribution of galaxies in halos of a given mass , 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 } \gtrsim 10 ^ { 14 } \ > h ^ { -1 } M _ { \odot } are red galaxies . These numbers decrease to 50 % and 40 % , respectively , in halos with M _ { h } \sim 10 ^ { 12 } \ > h ^ { -1 } M _ { \odot } . 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 } \ > h ^ { -1 } M _ { \odot } , 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 } \lesssim 10 ^ { 14.0 } \ > h ^ { -1 } M _ { \odot } , 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 } \geq 0.8 , ranges from \sim 2.5 \% for groups with M _ { h } \sim 10 ^ { 14 } \ > h ^ { -1 } M _ { \odot } to 18-60 % for groups with M _ { h } \sim 10 ^ { 13 } \ > h ^ { -1 } M _ { \odot } . The number distribution of satellite galaxies in groups of a given mass follows a Poisson distribution , in agreement with the occupation statistics of dark matter sub-halos . This provides strong support for the standard lore that satellite galaxies reside in sub-halos . Finally , we measure the fraction of satellites , which changes from \sim 5.0 \% for galaxies with \ > { } ^ { 0.1 } { M } _ { r } -5 \log h \sim - 22.0 to \sim 40 \% for galaxies with \ > { } ^ { 0.1 } { M } _ { r } -5 \log h \sim - 17.0 .