Distribution of the observed stars in E-L_z-L_⊥ spaces. Stars associated with Thamnos and GSE by Dodd et al. (2023) are plotted in purple and green, respectively. Stars from Paper I are reported in background as grey points. The colour coding of the border of these points reflect the association provided in Paper I: dark green for GSE, brown for Sequoia, blue for Antaeus, magenta for ED-2, orange for ED-3, and grey for stars that are not associated with any substructure.