The first group is the Superclass Agnatha. This group is the most primitive of the three groups of fishes. The fish belonging to this group have no jaws. Their mouth is like a hole in the head that lacks moveable parts. Lamprays and hagfishes are the only surviving fish of this type.
The sharks, rays, and chimaeras make up the second group of fishes, the Class Chondrichthyes.
The third major group of fishes is the Osteichthyes or the true bony fish, which is divided into two classes. The first class is the more primitive of the two classes and is called the Sarcopterygii. This class contains fish such as the coelacanths and the lungfishes.