For finite groups, we investigate both converse Lagrange theorem (CLT) orders and supersolvable (SS) orders, and see that the latter form a proper subset of the former. We focus on the difference between these two sets of orders, reformulate the work of earlier authors algorithmically, and construct a computer program to enumerate such NSS-CLT orders. We establish several results relating to NSS and CLT orders and, working from our computer-generated data, propose a pair of conjectures and obtain a complete characterization of the most common form of NSS-CLT order.