Very clever! I was able to name every group but ended up with even numbers amongst triangular and was unable to separate them. Happy with 6/10

I'm loathe to suffer puzzles which have multiple valid solutions - red herrings are par for the course, but usually by their nature the red herring group is impossible to take since the puzzle would be unsolvable.

In this case, there was no particular reason that "multiples of three" wasn't an eligible group in my mind (3-6-12-15), with 2-8-10-14 forming a neat set of even numbers - then Prime and Square would remain as is. Put short: Blech.

Not for me this one. Multiple ways to solve with valid reasoning. At its simplest; this group are the 4 lowest numbers. This group are the 4 highest numbers. Split the others into even and odd. Voila!