Cryptodira is the group that consists of all turtles who pull their necks straight back into their shell (and Sea Turtles). They are usually called "Hidden-necks". They have what is called an "S-neck", so named because, if you look at their skeleton, their neck forms an 's' shape when inside of the shell (I'll add images in the future). There are no more clade-specific groups anymore, so you will no longer see my lists of notable clade-only members. But that is good because you can quickly move through the hyperlinks! Also, from here, the main source of debate is over Linnaean vs PhyloCode classification. I will do my best to keep track of both, but I will default to Linnaean if I need to! (Again, if you see a problem or any misinformation, send a DM to me in Discord)
cryptodira branches off into 2 Infraorders: