Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11750944 | C2 | semidirect |
| 2. #11750796 | C2 | semidirect |
| 3. C8×D60 | C2 | semidirect |
| 4. C3×C5×#335 | C2 | semidirect |
| 5. #11746306 | C2 | semidirect |
| 22. C5×#335 | D3 | semidirect |
| 43. C3×#335 | D5 | semidirect |
| 69. D60 | D8 | semidirect |
| 74. C3×C5×C8 | D8 | semidirect |
| 106. #335 | D15 | semidirect |
| 154. C5×C8 | D24 | semidirect |
| 189. C3×C8 | D40 | semidirect |
| 220. C3×C5 | #1667 | semidirect |
| 257. C8 | D120 | semidirect |
| 263. C5 | #68576 | semidirect |
| 277. C3 | #10599369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750944 | 2 |
| #11750796 | 2 |
| C8×D60 | 2 |
| C3×C5×#335 | 2 |
| #11746306 | 2 |
| #10599369 | 3 |
| #68576 | 5 |