Typically, fish are categorized into three classes: superclass Agnatha (fish without jaws), class Chondrichthyes (fish with cartilage), and superclass Osteichthyes (bony fishes).
All jawed vertebrates fall to the infraphylum Gnathostomata, which also includes the latter two categories.
Agnatha:
The skin of early animals possessed thick bony scales and plates, but they are no longer present in contemporary species.
The skeleton is cartilaginous in most instances.
The notochord of the embryo survives until adulthood.
There are seven or more paired gill pouches.
Eg .Hagfishes, Lampreys
Osteichthyes:
Osteichthyes order has a bony endoskeleton. It is the biggest group of vertebrates and has a wide variety of freshwater and marine bony fishes.
The following characteristics are shared by all bony fishes: a bony skeleton, scales, paired fins, one set of gill openings, jaws, and paired nostrils.
Eg. Queensland lungfish, American black surgeon.
Chondrichthyes:
Fish belonging to the Chondrichthyes order have cartilaginous endoskeletons.
The majority of them are marine fish.
They contain a pair of powerful jaws and the mouth is present ventrally.
They contain 5-7 pairs of gills. Gaseous exchange occurs through the water current that passes over the gills.
They lack air bladders so they swim actively to avoid sinking.