Hydrans were notable to breathe methane, which could be uncomfortable or lethal for most Federation species. They had three arms, legs and eyes, as well as a tough, leathery skin. They had three sexes: male, female and matriarchal, only two of which are sentient. All births resulted in multiples of 3 (at least one of each sex) who are taken care of by the Matriarchals. (TOS games: Starfleet Command (game), Starfleet Command Volume II: Empires at War)
Males tended to dominate command-level positions, as well as science and engineering, while females tend to form up most of the worker classes, as well as marines and fighter pilots. Some females could hold command positions (usually within fighter squadrons), or even the throne. Matriarchals were non-sentient and were homemakers.
Their culture was deeply religious and their religion bordered on animism, as each household, starship, squadron and fleet possessed a god or a set of gods. Some gods were of a higher order, but what gods were put in the public limelight were decided by what groups came to power. Even with Hydran religion, the Hydrans were similar in disposition to the Federation concerning diplomacy and exploration so that, when they weren't at war, they were out there exploring the galaxy for scientific purposes.
Hydran warships usually came in three flavors: fusion beam-armed carriers for close combat, hellbore cannon-armed ships for long-ranged combat and orbital bombardment and, finally, command cruisers as well as explorers with mixed weaponry. Also, Hydrans were among the first to develop ablative armor and Hydran ships were usually built to last a long time, if not for combat. They also designed their ships for continuous operation under maximum evacuation capacity. Its shipbuilding culture was also marked by a never-ending desire of greater MEC per unit of mass. (RIS Bouteina: "Fury of the Prison Ships")