Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×D3×D40 | C2 | semidirect |
| 2. C2×C3×D80 | C2 | semidirect |
| 3. #11747915 | C2 | semidirect |
| 4. C2×#90938 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. #11745892 | C2 | semidirect |
| 13. C2×C3×D40 | C22 | semidirect |
| 18. C2×C3×C5×C16 | C22 | semidirect |
| 19. #91102 | C22 | semidirect |
| 20. C2×C5×C3⋊C16 | C22 | semidirect |
| 28. C2×D80 | D3 | semidirect |
| 44. D120 | D4 | semidirect |
| 51. C3×D40 | D4 | semidirect |
| 62. (C2×D3)⋊C16 | D5 | semidirect |
| 71. C2×D40 | C2×D3 | semidirect |
| 73. C2×C5×C16 | C2×D3 | semidirect |
| 112. C2×C3×C16 | C2×D5 | semidirect |
| 116. C2×C3⋊C16 | C2×D5 | semidirect |
| 138. D40 | #67 | semidirect |
| 154. C2×C5×D3 | D16 | semidirect |
| 225. C2×C16 | D3×D5 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 314. C2×D3 | D80 | semidirect |
| 356. C5 | #71467 | semidirect |
| 375. C3 | #10599901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D40 | 2 |
| C2×C3×D80 | 2 |
| #11747915 | 2 |
| C2×#90938 | 2 |
| #11746330 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| #11745892 | 2 |
| #10599901 | 3 |
| #71467 | 5 |