Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
540 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 82 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×#5683 | C2 | semidirect |
| 2. C5×#5061 | C2 | semidirect |
| 3. C5×#4741 | C2 | semidirect |
| 4. C3×C5×#354 | C2 | semidirect |
| 5. C5×#4471 | C2 | semidirect |
| 20. #69154 | C5 | direct (N × H) |
| 24. C5×#354 | D3 | semidirect |
| 26. C23×C5×D3 | D4 | semidirect |
| 27. C2×C3×C5×Q8 | D4 | semidirect |
| 40. C3×C42×C5 | D4 | semidirect |
| 41. C5×#217 | D4 | semidirect |
| 50. #5683 | C2×C5 | semidirect |
| 51. #5061 | C2×C5 | semidirect |
| 52. #4741 | C2×C5 | semidirect |
| 53. C3×#354 | C2×C5 | semidirect |
| 54. #4471 | C2×C5 | semidirect |
| 110. C2×C5×Q8 | D12 | semidirect |
| 129. C42×C5 | D12 | semidirect |
| 133. #354 | C5×D3 | semidirect |
| 151. C23×D3 | C5×D4 | semidirect |
| 152. C2×C3×Q8 | C5×D4 | semidirect |
| 165. C3×C42 | C5×D4 | semidirect |
| 166. #217 | C5×D4 | semidirect |
| 261. C2×Q8 | C5×D12 | semidirect |
| 280. C42 | C5×D12 | semidirect |
| 281. C3×C5 | #2199 | semidirect |
| 332. C5 | #69154 | direct (N × H) |
| 349. C3 | C5×#2199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| C5×#5061 | 2 |
| C5×#4741 | 2 |
| C3×C5×#354 | 2 |
| C5×#4471 | 2 |
| C5×#2199 | 3 |
| #69154 | 5 |