Some shorthand notation used here:
- Sk stands for k^2/[(k-1)(k+1)] by standard convention.
- Tk = Sk * S(k+1) stands for [k(k+1)/2]/[(k-1)(k+2)/2].
- Lp refers to the p-limit, i.e. the subgroup of primes less than or equal to p.
- Lp(-q) refers to the p limit with the prime q omitted: e.g. L17(-11) refers to the 2.3.5.7.13.17 subgroup; these omissions can be stacked so that L23(-5.17) refers to the group 2.3.7.11.13.19.23.
This list eventually aims to be complete to the semi-41-limit, i.e. the class of subgroups with at most one prime greater than 41.
2- and 3-prime subgroups (2.3 and 2.3.p)
Note that the following lists are complete and the insertion of higher primes will add no new inclusions to them.
2-prime subgroup (2.3)
| Square-particular
|
Subgroup
|
Comma
|
| Ratio
|
Smonzo
|
| S2
|
2.3
|
4/3
|
[2 -1⟩
|
| S3
|
2.3
|
9/8
|
[-3 2⟩
|
| Triangle-particular
|
Subgroup
|
Comma
|
| Ratio
|
Smonzo
|
| T2
|
2.3
|
3/2
|
[-1 1⟩
|
3-prime subgroups (2.3.p)