What is the complete order of ranks in 13-card lowball?

[MarkGritter]

If you're playing 13-card lowball, then A23456789TJQK is the best hand. Obviously pairs are worse, then two pair. Trips are worse than one pair or two pair, but are they worse than three pair? Quads are worse that trips or trips + a pair, but what about two trips?

How would you order the complete set of 13-card lowball hands? A hand may have 0-2 quads, 0-4 trips, and 0-6 pairs (though obviously not all at the same time.)