Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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×C5×#500 | C2 | semidirect |
| 4. #11746368 | C2 | semidirect |
| 5. #11746278 | C2 | semidirect |
| 19. C5×#500 | D3 | semidirect |
| 38. C3×#500 | D5 | semidirect |
| 67. C3×C5×C8 | SD16 | semidirect |
| 95. #500 | D15 | semidirect |
| 136. C5×C8 | #215 | semidirect |
| 166. C3×C8 | #688 | semidirect |
| 193. C3×C5 | #1693 | semidirect |
| 222. C8 | #6717 | semidirect |
| 227. C5 | #71373 | semidirect |
| 238. C3 | #10602166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| #11751184 | 2 |
| #11750789 | 2 |
| #11746368 | 2 |
| #11746278 | 2 |
| #10602166 | 3 |
| #71373 | 5 |