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We search for dynamical substructures in the LAMOST DR3 very metal-poor (VMP) star catalog. After cross-matching with Gaia DR2, there are 3300 VMP stars with available high-quality astrometric information that have halo-like kinematics. We apply a method based on self-organizing maps to find groups clustered in the 4D space of orbital energy and angular momentum. We identify 57 dynamically tagged groups, which we label DTG-1 to DTG-57. Most of them belong to existing substructures in the nearby halo, such as the $Gaia$ Sausage or Sequoia. The stream identified by Helmi et al. is recovered, but the two disjoint portions of the substructure have distinct dynamical properties. The very retrograde substructure Rg5 found previously by Myeong et al. is also retrieved. We report 6 new DTGs with highly retrograde orbits, 2 with very prograde orbits, and 12 with polar orbits. By mapping other datasets (APOGEE halo stars, and catalogs of r-process-enhanced and CEMP stars) onto the trained neuron map, we can associate stars with detailed chemical abundances to the DTGs, and look for associations with chemically peculiar stars. The highly eccentric $Gaia$ Sausage groups contain representatives both of debris from the satellite itself (which is $\alpha$-poor) and the Splashed Disk, sent up into eccentric halo orbits from the encounter (and is $\alpha$-rich). The new prograde substructures also appear to be associated with the Splashed Disk. The DTGs belonging to the $Gaia$ Sausage host two relatively metal-rich $r$-II stars and six CEMP stars in different sub-classes, consistent with the idea that the $Gaia$ Sausage progenitor is a massive dwarf galaxy. Rg5 is dynamically associated with two highly $r$-process-enhanced stars with [Fe/H] $\sim -$3. This finding indicates that its progenitor might be an ultra-faint dwarf galaxy that has experienced $r$-process enrichment from neutron star mergers.