sympathetic nasal

There's a verb root (that's even more basic than a "stem" right?) "puth" ... now in the present, it gets "-an-" added to make up the stem, along with a "sympathetic nasal" before the "th." So "puth" becomes (in the present) "punthan-xxx." And other principal parts are clearly derived from "puth," rather than "punthan-." In other words, the present tense (which we naturally take as the basic, most primitive version) has evolved away from the root, while the other principal parts have stayed closer to it.

It's also called "nasal infix."