What fish group has skeletons made mostly of cartilage rather than bone?

The fish group with skeletons made mostly of cartilage rather than bone is cartilaginous fish.

Cartilaginous fish belong to the class Chondrichthyes, whose living members include sharks, rays, skates, sawfish, and chimaeras. Their internal skeletons are primarily cartilage, a firm but flexible tissue. This differs from bony fish, classified broadly among Osteichthyes, whose skeletons are primarily made of bone.

The group has other distinctive traits as well. Most sharks and rays have tooth-like placoid scales, no swim bladder, and internal fertilization. Instead of relying on a swim bladder for buoyancy, many sharks use large oil-rich livers and lift generated by swimming. Their gill openings are also generally more visible than those of bony fish.

A common mix-up is treating “cartilaginous fish” as meaning fish with no backbone. Chondrichthyans do have a vertebral column, although it is made largely of cartilage; the name refers to the material of the skeleton, not the absence of a spine. “Jawless fish,” such as lampreys, are a separate lineage.