In a recent paper we have shown that the possibility of including heavy flavor in the dibaryon sector can lead to some new favored configurations (relative to the baryon-baryon threshold). In this study we extend our previous work by a systematic study of all the physical Qq5 systems in a simple chromomagnetic model. In the first part we assume that the q quarks belong to the fundamental irrep of SU(3)F and that the Q quark has infinite mass. These assumptions are subsequently relaxed by introducing two mass parameters δ and η. Once these symmetries are broken we gain access in our model to a large number of new dibaryons containing heavy flavor. Some of them could be stable against decay via strong interactions, and we indicate the most favorable cases.