Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11753961 | C2 | semidirect |
| 2. C3×#65186 | C2 | semidirect |
| 3. #11747543 | C2 | semidirect |
| 4. C2×#90937 | C2 | semidirect |
| 5. #11746318 | C2 | semidirect |
| 6. C5×#4495 | C2 | semidirect |
| 7. #11745885 | C2 | semidirect |
| 13. C2×C3×D40 | C22 | semidirect |
| 19. C3×C5×#108 | C22 | semidirect |
| 20. C2×C3⋊#672 | C22 | semidirect |
| 21. C5×#812 | C22 | semidirect |
| 30. #65186 | D3 | semidirect |
| 67. #4495 | D5 | semidirect |
| 76. C2×D40 | C2×D3 | semidirect |
| 79. C5×#108 | C2×D3 | semidirect |
| 119. C3×#108 | C2×D5 | semidirect |
| 124. #812 | C2×D5 | semidirect |
| 237. #108 | D3×D5 | semidirect |
| 307. C3×C5 | #2192 | semidirect |
| 355. C5 | #71094 | semidirect |
| 368. C3 | #10600051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11753961 | 2 |
| C3×#65186 | 2 |
| #11747543 | 2 |
| C2×#90937 | 2 |
| #11746318 | 2 |
| C5×#4495 | 2 |
| #11745885 | 2 |
| #10600051 | 3 |
| #71094 | 5 |