Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
672 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 94 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. D12×D20 | C2 | semidirect |
| 2. C5×#4843 | C2 | semidirect |
| 3. #11747029 | C2 | semidirect |
| 4. #11747026 | C2 | semidirect |
| 5. #11746306 | C2 | semidirect |
| 6. C3×#64703 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 13. C5×#874 | C22 | semidirect |
| 21. C3×C5×C4⋊C8 | C22 | semidirect |
| 22. C4⋊(C3⋊#168) | C22 | semidirect |
| 24. C3×C4×#168 | C22 | semidirect |
| 33. #64703 | D3 | semidirect |
| 65. #4843 | D5 | semidirect |
| 82. C5×C4⋊C8 | C2×D3 | semidirect |
| 86. C4×#168 | C2×D3 | semidirect |
| 110. C5×D12 | D8 | semidirect |
| 115. C3×D20 | D8 | semidirect |
| 133. #874 | C2×D5 | semidirect |
| 135. C3×C4⋊C8 | C2×D5 | semidirect |
| 255. D20 | D24 | semidirect |
| 274. C4⋊C8 | D3×D5 | semidirect |
| 314. D12 | #686 | semidirect |
| 370. C3×C5 | #1619 | semidirect |
| 441. C5 | #68194 | semidirect |
| 463. C3 | #10601808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D12×D20 | 2 |
| C5×#4843 | 2 |
| #11747029 | 2 |
| #11747026 | 2 |
| #11746306 | 2 |
| C3×#64703 | 2 |
| #11745837 | 2 |
| #10601808 | 3 |
| #68194 | 5 |