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We construct mock catalogs of galaxy groups using subhalo abundance matching(SHAM) and undertake several new tests of the SHAM prescription for thegalaxy-dark matter connection. All SHAM models we studied exhibit significanttension with galaxy groups observed in the Sloan Digital Sky Survey (SDSS). TheSHAM prediction for the field galaxy luminosity function (LF) is systematicallytoo dim, and the group galaxy LF systematically too bright, regardless of thedetails of the SHAM prescription. SHAM models connecting r-band luminosity, Mr,to Vacc, the maximum circular velocity of a subhalo at the time of accretiononto the host, faithfully reproduce galaxy group abundance as a function ofrichness, g(N). However, SHAM models connecting Mr with Vpeak, the peak valueof Vmax over the entire merger history of the halo, over-predict galaxy groupabundance. Our results suggest that no SHAM model can simultaneously reproducethe observed g(N) and two-point projected galaxy clustering. Nevertheless, wealso report a new success of SHAM: an accurate prediction for Phi(m12), theabundance of galaxy groups as a function of magnitude gap m12, defined as thedifference between the r-band absolute magnitude of the two brightest groupmembers. We show that it may be possible to use joint measurements of g(N) andPhi(m12) to tightly constrain the details of the SHAM implementation.Additionally, we show that the hypothesis that the luminosity gap isconstructed via random draws from a universal LF provides a poor description ofthe data, contradicting recent claims in the literature. Finally, we test acommon assumption of the Conditional Luminosity Function (CLF) formalism, thatthe satellite LF need only be conditioned by the brightness of the centralgalaxy. We find this assumption to be well-supported by the observed Phi(m12).

SHAM Beyond Clustering: New Tests of Galaxy-Halo Abundance Matching with Galaxy Groups