I've been working on a classification of Bol loops of small order. Here is a list of the 3 Bol loops of order 15. This includes the cyclic group of order 15 and the 2 non-associative Bol loops of order 15 (neither of which is Moufang). The two non-associative examples are isotopic to one another. The completeness of this list was first shown by Niederreiter and Robinson (1981).
I have made available
In listing elements of the commutator (resp. associator) subloop of each of these loops, we have printed in italics
any elements which are not actual commutators (resp. associators). (I haven't checked, however, whether in fact this
phenomenon occurs among any the loops of order 15 in our list.)
The 2 Isotopy Classes of Bol Loops
Isotopy Class 0: The Cyclic Group 126.96.36.199
Isotopy Class 1: The 2 Non-Moufang (non-associative) Bol Loops 188.8.131.52, 184.108.40.206