Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C5×#4680 | C2 | semidirect |
| 5. C3×#64677 | C2 | semidirect |
| 6. #11745862 | C2 | semidirect |
| 7. #11745858 | C2 | semidirect |
| 31. #64677 | D3 | semidirect |
| 53. #4680 | D5 | semidirect |
| 88. C3×C5×C8 | SD16 | semidirect |
| 177. C5×C8 | #204 | semidirect |
| 217. C3×C8 | #688 | semidirect |
| 249. C3×C5 | #1671 | semidirect |
| 284. C8 | #6660 | semidirect |
| 289. C5 | #68537 | semidirect |
| 302. C3 | #10602137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C5×#4680 | 2 |
| #11747087 | 2 |
| #11746885 | 2 |
| C3×#64677 | 2 |
| #11745862 | 2 |
| #11745858 | 2 |
| #10602137 | 3 |
| #68537 | 5 |