Now this is where the information will become more readily available. Testudines are considered the clade for all "modern" turtles. This is why the scientific name for turtles (in a general sense) is "Testudine". In most papers, Testudine immediately branches off into Pleurodira and Cryptodira. However, some papers have species that don't fit in to the Cryptodira or Pleurodira clade, so I will list them here (remember, there is a lot of controversy in this area, so some of the groups listed in Testudinata are also listed here... yeah, I'm sorry.):
They both have two names because some people put "Pan-" as the overarching and some put "Para-" as the overarching, so, to save myself from more work, they link to the same page!
As mentioned earlier, Testudines immediately branches off into 2 suborders: