Lopingian taxonomic orders

Therapsida is a clade comprising a major group of eupelycosaurian synapsids that includes mammals and their ancestors and close relatives. Many of the traits today seen as unique to mammals had their origin within early therapsids, including limbs that were oriented more underneath the body, resulting in a more "standing" quadrupedal posture, as opposed to the lower sprawling posture of many reptiles and amphibians.

The order Notostraca, containing the single family Triopsidae, is a group of crustaceans known as tadpole shrimp or shield shrimp. The two genera, Triops and Lepidurus, are considered living fossils, with similar forms having existed since the end of the Devonian, around 360 million years ago. They have a broad, flat carapace, which conceals the head and bears a single pair of compound eyes. The abdomen is long, appears to be segmented and bears numerous pairs of flattened legs. The telson is flanked by a pair of long, thin caudal rami. Phenotypic plasticity within taxa makes species-level ide

Hybodontiformes, commonly called hybodonts, are an extinct group of shark-like cartilaginous fish (chondrichthyans) which existed from the late Devonian to the Late Cretaceous. Hybodonts share a close common ancestry with modern sharks and rays (Neoselachii) as part of the clade Euselachii. They are distinguished from other chondrichthyans by their distinctive fin spines and cephalic spines present on the heads of males. An ecologically diverse group, they were abundant in marine and freshwater environments during the late Paleozoic and early Mesozoic, but were rare in open marine environments

right|thumb|Helicoprion bessonovi, teeth at the front of the lower jaw (reversed for more natural position) 225px|thumb|Restoration of Romerodus ([[Caseodontidae)]]

Xenacanthiformes (or Xenacanthida) is an order or superorder of extinct shark-like chondrichthyans (cartilaginous fish) known from the Carboniferous to the Late Triassic. They were native to freshwater, marginal marine, and shallow marine habitats. Some xenacanths may have grown to lengths of . Most xenacanths died out at the end of the Permian in the End-Permian Mass Extinction, with only a few forms surviving into the Triassic.

Eosuchia is a proposed order of extinct diapsid reptiles comprising taxa from the Permian and Triassic. Eosuchia was initially defined to include all "thecodontian" reptiles which did not have an antorbital fenestra but did retain tabulars, postparietals, and a large pineal foramen (Broom, 1914). Broom coined the term as a new suborder for Youngina.

Synechodontiformes is an extinct order of prehistoric shark-like cartilaginous fish, known from the Permian to the Paleogene. They are considered to be members of Neoselachii, the group that contains modern sharks and rays.