With the exception of a trailer with a GVW of 10k or more, as I remember it. Then you're looking at a Non-CDL Class A.
Incorrect. As long as the Total GVWR of the combination is less than 26,001lbs you are safe.
For example; if my tow rig has a GVWR of 10k, I can tow a trailer with a GVWR of 16k legally with a Class C.