Okay, start with the common ancestor of all vertebrates.
The first group to split off gave rise to the modern hagfish, or “slime eel”, a noxious ectoparasite which had a cranium but no vertebrae. Everything else, from lampreys to llamas, is more closely related to each other than any of them are to the hagfish.
The next few groups to split off were the “jawless fish,” including 2. the modern lamprey; 3. the conodont animals (eel-haped filter feeders whose only hard part was the bony framework for the filter apparatus, the so-called conodonts; 4. the Osteostracans, 5. the Heterostracans, and 6. the Anaspids, all three of which were bony-armored groups of jawelss fish on three distinct body plans, each of which radiated into three or four major subgroups. There were also a couple of 7-8. minor groups of jawless fish. Paleontologists will argue at inordinate length about which of these diverged before which others; the sequence I listed them gives one of several common orders of divergence.
This now leaves us with the Gnathostomes, the jawed vertebrates. First group to split off here is 9. the Acanthodians, the so-called “spiny sharks” of the Paleozoic. (Though definitely spiny, they were not sharks.) Next probably was 10. the Placoderms, a large array of armored Paleozoic fish including the Arthrodires and the Antiarchs. Some exxperts don’t believe the Placoderms are a natural group, but rather a lumping together of several lineages of jawed fish that didn’t survive.
- Next group to split off were the Chondrichthyes, the cartiliginous fish. This includes two main groups (which may be closely related separate groups), the Holocephalians which are made up of the chimeras or ratfish and two extinct related groups, and the Selachians, which include primitive extinct sharks, modern sharks, skates, rays, the dogfish, the sawfish, etc.
What we’re left with at that point is the Osteichthyes, including on the one hand the Actinopterygians, the ray-finned fish that constitute most modern bony fish, and on the other the Sarcopterygians, including a wide range of extinct forms, the three lungfish, the coelacanth, and all tetrapods (land vertebrates).
We can break this stuff down into more detail, but the fact of the matter is that the goldfish, the sturtgeon, the marlin, the lungfish, the snake, frog, the dinosaur, the sparrow, and you and me, are all more closely related to each other than any of them is to the shark – and more closly related to the shark than to the lamprey or any of the extinct forms noted above.