Recent studies have revealed that the Milky Way's stellar halo is a composite of stellar populations of different origins, including multiple accretion events. To better understand how the Milky Way and other spiral galaxies were formed, it is necessary to thoroughly characterize the chemical and kinematic properties of these structures. We search for kinematic structures of the stellar halo to find any substructures within them (when indeed present) and charac- terize the chemodynamical properties of the identified groups with the GALAH DR4 and Gaia surveys. We applied wavelet transforms in the space defined by a square root of radial action (Jr) and azimuthal action (Lz) to search for kinematic overdensities. Then, we selected stars in the detected structures and investigated their elemental abundances to determine their origin. Additionally, we checked for any contamination from other stellar populations within the detected groups with the unsupervised machine learning algorithm t-Distributed Stochastic Neighbor Embedding (t-SNE), for which we performed chemical tagging in a high-dimensional parameter space using 15 elemental abundances as input. We recovered five kinematic structures in the action space with the wavelet transform. These groups are the Galactic disk, Splash, Gaia-Sausage-Enceladus (GSE), Thamnos1, and Thamnos2. We found that GSE has two peaks with the wavelet transform. One of these peaks is located at SQRT(Jr)~=25kpc.km/s and is a result of contamination from disk stars. The other peak corresponds to the "cleanest" GSE population and is located above SQRT(Jr)~=40kpc.km/s. We also detected three peaks in Thamnos. We linked two of them to Thamnos1, while the peak with the stars on the most retrograde orbits was linked to Thamnos2. The t-SNE algorithm confirmed these findings. We also analyzed individual elemental abundances of each group and found that Thamnos2 has a higher [alpha/Fe] ratio than the other groups and that iron-peak elements are more abundant in the Splash than in the halo groups, while the halo structures retain a higher r-process signature than the splashed disk. A multiply peaked substructure we observe in action space in GSE and Thamnos suggests that the splashed disk extends beyond the borders of prograde orbits. Each of the four halo groups studied in this paper have unique chemodynamical properties that confirm their extra-galactic origin.