Is there a characterization of CI-groups of order less than 100?

We know some benefit criterion in articles such as:

C‎. ‎H‎. ‎Li‎, ‎On isomorphisms of finite Cayley graphs-a survey‎, ‎Discrete Math.‎, ‎256 (2002) 301-334‎.

C‎. ‎H‎. ‎Li‎, ‎Z‎. ‎P‎. ‎Lu‎, ‎P‎. ‎P‎. ‎Pa'lfy‎, ‎Further restrictions on the structure of finite CI-groups‎, ‎J‎. ‎Algebraic Combin.‎, ‎26 (2007) 161-181‎.‎

Now, do you know which finite groups of order less than 100 are CI-groups?

For example, which groups of order 30 are CI-groups?

• For completeness, a finite group is called CI if for any 2 symmetric subsets $S,T$ such that no automorphism of $G$ maps $S$ to $T$, the corresponding Cayley graphs (with no orientation, labeling, or multiple loops) are non-isomorphic. – YCor Apr 16 '16 at 16:37
• I saw a talk about this recently, and there are certainly some open cases of order less than $100$. On the other hand, it is easy to find the answer by brute-force (by computer) up to order $50$ or $60$ or so. In particular, $30$ is certainly "known". (In the sense that some people know the answer, although it might not be in the literature.) – verret Apr 16 '16 at 22:38