  The study of cluster substructures is important for the determination of the
cluster dynamical status, assembly history, and the evolution of cluster
galaxies, and it allows to set of constraints on the nature of dark matter and
cosmological parameters. We present and test DS+, a new method for the
identification and characterization of group-sized substructures in clusters.
Our new method is based on the projected positions and line-of-sight velocities
of cluster galaxies, and it is an improvement and extension of the traditional
method of Dressler & Shectman (1988). We test it on cluster-size cosmological
halos extracted from the IllustrisTNG simulations, with virial masses $\rm{14
\lesssim \log (M_{200}/M_{\odot}) \lesssim 14.6}$, that contain on average
$\sim 190$ galaxies. We also present an application of our method on a real
data set, the Bullet cluster. DS+ is able to identify $\sim 80\%$ of real group
galaxies as members of substructures, and at least 60\% of the galaxies
assigned to substructures belong to real groups. The physical properties of the
real groups are significantly correlated with those of the corresponding
detected substructures, albeit with significant scatter, and overestimated on
average. Application of the DS+ method to the Bullet cluster confirms the
presence and main properties of the high-speed collision and identifies other
substructures along the main cluster axis. DS+ proves to be a reliable method
for the identification of substructures in clusters. The method is made freely
available to the community as a Python code.
