The AZA has spent recent years making a lot of moves in the population as unidentified individuals become of a known species. There are still quite a few unknown individuals about (often due to poor record keeping) as well as many hybrids. In relative order of rarity, here is what‘s kept (it would be impractical to list all the institutions with each species)
C. microphyes (Volcán Darwin giant tortoise)
Unidentified/hybrids
C. porteri (western Santa Cruz giant tortoise)
C. vicina (Iguana Cove tortoise)
C. vandenburghi (Volcán Alcedo giant tortoise)
C. becki (Volcán Wolf giant tortoise)
C. darwini (Santiago giant tortoise)
C. guentheri may also be kept, but it’s hard to tell due to conflicting records. Breeding program success is mostly limited to microphyes and porteri, at the moment, with a few zoos especially being successful with them (for example, Gladys Porter with microphyes and Riverbanks with porteri).