Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
408 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. C8×D60 | C2 | semidirect |
| 2. C3×#64984 | C2 | semidirect |
| 3. #11747043 | C2 | semidirect |
| 4. C5×#4458 | C2 | semidirect |
| 5. #11745852 | C2 | semidirect |
| 20. #64984 | D3 | semidirect |
| 44. #4458 | D5 | semidirect |
| 64. D60 | D8 | semidirect |
| 73. C3×C5×C8 | D8 | semidirect |
| 154. C5×C8 | #213 | semidirect |
| 188. C3×C8 | D40 | semidirect |
| 220. C3×C5 | #1667 | semidirect |
| 257. C8 | #6653 | semidirect |
| 263. C5 | #71282 | semidirect |
| 277. C3 | #10599369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C3×#64984 | 2 |
| #11747043 | 2 |
| C5×#4458 | 2 |
| #11745852 | 2 |
| #10599369 | 3 |
| #71282 | 5 |