Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 98 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. C5×#4838 | C2 | semidirect |
| 3. C3⋊C8×D20 | C2 | semidirect |
| 4. #11746301 | C2 | semidirect |
| 5. C3×#64703 | C2 | semidirect |
| 6. #11745837 | C2 | semidirect |
| 7. #11745831 | C2 | semidirect |
| 29. #64703 | D3 | semidirect |
| 53. #4838 | D5 | semidirect |
| 86. C3×D20 | M16 | semidirect |
| 182. D20 | ΓL(1,𝔽25) | semidirect |
| 267. C3×C5 | #1586 | semidirect |
| 314. C5 | #68157 | semidirect |
| 329. C3 | #10601656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4838 | 2 |
| C4×#6652 | 2 |
| C3⋊C8×D20 | 2 |
| #11746301 | 2 |
| C3×#64703 | 2 |
| #11745837 | 2 |
| #11745831 | 2 |
| #10601656 | 3 |
| #68157 | 5 |