We present the results of a Parkes Multibeam HI survey of six loose groups of galaxies analogous to the Local Group. This survey was sensitive to HI-rich objects in these groups to below 107M· of HI, and was designed to search for low mass, gas-rich satellite galaxies and potential analogs to the high-velocity clouds seen around the Milky Way. This survey detected a total of 79 HIrich objects associated with the six groups, half of which were new detections. While the survey identified a small number of dwarf galaxies, no star-free HI clouds were discovered. The HI mass function of the six groups appears to be roughly flat as is that of the Local Group. The cumulative velocity distribution function (CVDF) of the HI-rich halos in the six groups is identical to that of the Local Group. Both of these facts imply that these groups are true analogs to the Local Group and that the Local Group is not unique in its lack of low-mass dwarf galaxies as compared to the predictions of cold dark matter models of galaxy formation. This survey also constrains the distance to and HI masses of the compact high-velocity clouds (CHVCs) around the Milky Way. The lack of CHVC analog detections implies that they are distributed within ≲160 kpc of the Milky Way and have average HI masses of ≲4×105M·. The spatial distribution of CHVCs is consistent with the predictions of simulations for dark matter halos. Furthermore the CVDF of Local Group galaxies plus CHVCs matches the predicted CVDF of cold dark matter simulations of galaxy formation. This provides circumstantial evidence that CHVCs may be associated with low-mass dark matter halos.