Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#65732 | C2 | semidirect |
| 2. #11751680 | C2 | semidirect |
| 4. #11746776 | C2 | semidirect |
| 5. #11746479 | C2 | semidirect |
| 6. #11746460 | C2 | semidirect |
| 7. #11746450 | C2 | semidirect |
| 19. #91111 | C4 | semidirect |
| 20. C5×#826 | C4 | semidirect |
| 21. #90947 | C4 | semidirect |
| 22. #90941 | C4 | semidirect |
| 26. #65732 | D3 | semidirect |
| 101. #826 | AGL(1,𝔽5) | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #70922 | semidirect |
| 282. C3 | #10604123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65732 | 2 |
| #11751680 | 2 |
| #11748277 | 2 |
| #11746776 | 2 |
| #11746479 | 2 |
| #11746460 | 2 |
| #11746450 | 2 |
| #10604123 | 3 |
| #70922 | 5 |