  We take advantage of the exquisite quality of the Hubble Space Telescope
26-filter astro-photometric catalog of the core of Omega 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 sub-populations also come to light.
In this way, we have identified at least 15 sub-populations, each of which has
a distinctive fiducial curve through our 5-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 Omega 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
most likely is associated with.
