Single-cell-resolved measurements reveal heterogeneous distributions of clathrin-dependent (CD) and -independent (CLIC/GEEC: CG) endocytic activity in Drosophila cell populations. dsRNA-mediated knockdown of core versus peripheral endocytic machinery induces strong changes in the mean, or subtle changes in the shapes of these distributions, respectively. By quantifying these subtle shape changes for 27 single-cell features which report on endocytic activity and cell morphology, we organize 1072 Drosophila genes into a tree-like hierarchy. We find that tree nodes contain gene sets enriched in functional classes and protein complexes, providing a portrait of core and peripheral control of CD and CG endocytosis. For 470 genes we obtain additional features from separate assays and classify them into early- or late-acting genes of the endocytic pathways. Detailed analyses of specific genes at intermediate levels of the tree suggest that Vacuolar ATPase and lysosomal genes involved in vacuolar biogenesis play an evolutionarily conserved role in CG endocytosis.