Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
546 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5912 | C2 | semidirect |
| 2. C2×C5×C8×A4 | C2 | semidirect |
| 3. C5×#5402 | C2 | semidirect |
| 4. C5×#5401 | C2 | semidirect |
| 5. C5×#5398 | C2 | semidirect |
| 15. #85440 | C5 | direct (N × H) |
| 17. C23×C5×C8 | D3 | semidirect |
| 37. #5912 | C2×C5 | semidirect |
| 38. C2×C8×A4 | C2×C5 | semidirect |
| 39. #5402 | C2×C5 | semidirect |
| 40. #5401 | C2×C5 | semidirect |
| 41. #5398 | C2×C5 | semidirect |
| 123. C2×C5×C8 | S4 | semidirect |
| 135. C23×C8 | C5×D3 | semidirect |
| 147. C5×A4 | #135 | semidirect |
| 248. C22×C5 | #904 | semidirect |
| 288. C2×C8 | C5×S4 | semidirect |
| 302. A4 | C5×#135 | semidirect |
| 348. C5 | #85440 | direct (N × H) |
| 359. C22 | C5×#904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5912 | 2 |
| C2×C5×C8×A4 | 2 |
| C5×#5402 | 2 |
| C5×#5401 | 2 |
| C5×#5398 | 2 |
| C5×#3050 | 3 |
| C5×#904 | 4 |
| #85440 | 5 |