SIMBAD references

We take advantage of the exquisite quality of the Hubble Space Telescope 26-filter astro-photometric catalog of the core of ω Cen presented in the first paper of this series and the empirical differential-reddening correction presented in the second paper in order to distill the main sequence into its constituent populations. To this end, we restrict ourselves to the five most useful filters: the magic "trio" of F275W, F336W, and F438W, along with F606W and F814W. We develop a strategy for identifying color systems where different populations stand out most distinctly, then we isolate those populations and examine them in other filters where their subpopulations also come to light. In this way, we have identified at least 15 subpopulations, each of which has a distinctive fiducial curve through our five-dimensional photometric space. We confirm the MSa to be split into two subcomponents, and find that both the bMS and the rMS are split into three subcomponents. Moreover, we have discovered two additional MS groups: the MSd (which has three subcomponents) shares similar properties with the bMS, and the MSe (which has four subcomponents) has properties more similar to those of the rMS. We examine the fiducial curves together and use synthetic spectra to infer relative heavy-element, light-element, and helium abundances for the populations. Our findings show that the stellar populations and star formation history of ω Cen are even more complex than inferred previously. Finally, we provide as a supplement to the original catalog a list that identifies for each star which population it is most likely associated with.