United Federation of Planets
From Star Trek: Theurgy Wiki
In 2379, cooperation took place between the crew of a Federation Starfleet vessel, the USS Enterprise., and Romulan forces to defeat the Praetor Shinzon, whose actions would have destroyed both Earth and the Romulan Star Empire. It was hoped that this would mark the beginning of an end to hostility between the Federation and the Romulans, marking the beginnings of détente with a traditional enemy of the Federation.
After the death of Shinzon, the initial approaches between the Federation and the Romulans were continued and a new task force led by the USS Titan was dispatched to the Romulan Neutral Zone in order to begin talks with the Romulans. The USS Theurgy was a part of this task force, yet regrettably, the attempt failed, and the consequence was the Romulan Civil War.
A human by the name Nanietta "Nan" Bacco from the Federation Member State of Cestus III was elected Federation President in October of 2379, serving through the sundering of the Romulan Star Empire. It was unknown if the parasitic aliens that had overtaken Starfleet Command had also infiltrated the Federation Council at that point.
These were the Federation member species as of 2381.
(Note: A few are not listed because they have no relevance to the Star Trek: Theurgy story.)