So far, all ships named in the story have belonged to the UHF.
The Sovereign has the prefix IGS. What ‘IG’ means is not known. (Arc 1-finale-premium-2/2)
Ascendant: Recruit training ship.
Ascendant of Flames
Black Sword: Escort ship Captain Cross requests in chapter 1-intermission-1.
Empyrean: Recruit training ship
Empyrean of Swords
Fanged Viper: Escort ship Captain Cross requests in chapter 1-intermission-1.
Hegemon: Recruit training ship.
Hegemony of Dusk
Imperator: Recruit training ship.
Imperator of Deserts
Imperator of Seas
Interlocutor: The ship used by Runepriest Vedun to reach the Sovereign.
Monarch: Sister ship to Sovereign. Lost.
Sovereign: The ship (and AI) that Thea is on for most of Arc 1 and Arc 2.
Transcendant: Recruit training ship.
Valiant Radiance: escort ship Captain Cross requests in chapter 1-intermission-1.