  It is often believed that isolated, compact groups of galaxies (CGs) are
special systems. But CGs have rarely been compared to regular groups, which are
selected very differently. We study the global properties of a subsample of 80
groups of four members (CG4s), as well as their correlations, within the HMCG
Hickson-like sample of compact groups, and compare them with those of the
regular groups of Lim et al.. The latter are split into three control samples,
complete in redshift and magnitude: one with the four brightest members, one
with the four closest members to the brightest group galaxy (BGG) with less
than three magnitudes in range (Control4Cs), and one with exactly four members
(RG4s). The vast majority of CG4s are located within regular groups, and a
large preponderance of the BGGs of these CG4s are the same as those of their
host groups. CG4s are smaller than the groups of all other samples and more
luminous than RG4s, both results as expected from their selection as high
surface brightness systems. However, CG4s have similar luminosities as
Control4Cs. CG4s also have higher velocity dispersions, probably because of a
too permissive redshift accordance criterion. The BGGs of CG4s are not more
dominant in luminosity than those of RG4s, but they are significantly more
offset relative to the group size, because the Lim groups are built around
their BGGs. In summary, compact groups have similar properties to the regular
groups of four galaxies and to the cores of regular groups, once selection
criteria of CGs are considered. A large fraction of CGs are the cores of
regular groups, isolated on the sky by construction, but rarely isolated in
real space (from simulations), indicating that they are often plagued by chance
alignments of host groups galaxies along the line of sight.
