The dominant paradigm in biological systematics now is Cladism, and so most dino sistes on the Web tend to be cladistically based. Cladism can get quite abstract and confusing, mainly because it is so abstract. Consider the cladistic definition of the Dinosauria.Dinosauria = all descendants of the most recent common ancestor of Triceratops and Neornithes (modern birds).
Triceratops is mentioned because it is a creature as far away on the dinosaur family tree from birds as can be, yet it it's skeleton is well-known so it can be compared and contrasted with other species. Neornithes or modern birds are mentioned beuse they are the most specialised descendents of the dinosaurs, and indeed the only living dinosaurian descendents.
From the above equation the various dinosaurian subtaxa can be deduced: e.g.Saurischia = Neornithes and all taxa closer to it than to Triceratops
From these basic clades, further subclades can be derived, and more subclades in rurn from them. There are no orders, suborders, etc. Families and subfamilies are retained only as a conventient way of linking two genera, and so used in a different manner to in the Linnean scheme. Attempts to reconcile the two systems are fraught with difficulties.
I find the whole thing is all incredibly abstract, although there is also a certain mathematical logic in it; it's like set theory. Instead of linnean categories such as "Dinosaura", (or "mammalia" "reptilia" or any other taxonomic grouping above species level), there is only a nested series of monophyletic clades, one within the other, like layers of an onion, all based on the idea of a MRCA (Most Recent Common Ancestor). The following links give some dinosaur cladogram trees for you to look at, all of which are based on these principles.
Classification - The Dinosauricon - T. Mike Keesey's gigantic cladogram!
Dinosauria Cladogram by Jeff Poling. Navigate your way through the dinosaur family tree
Mikko's Phylogeny includes not only Dinosaurs but every other type of living being!
Thescelosaurus! Justin Tweet's site includes both cladograms and a short but very useful description of each species
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