Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 106 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×C5×D3×D8 | C2 | semidirect |
| 2. C2×C3×C5×D16 | C2 | semidirect |
| 3. C5×#5157 | C2 | semidirect |
| 4. C2×C5×#826 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. C5×#4509 | C2 | semidirect |
| 7. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 11. C2×C3×C5×D8 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 22. C5×#818 | C22 | semidirect |
| 23. C2×C5×C3⋊C16 | C22 | semidirect |
| 24. #71467 | C5 | direct (N × H) |
| 27. C2×C5×D16 | D3 | semidirect |
| 44. C3×C5×D8 | D4 | semidirect |
| 51. C5×D24 | D4 | semidirect |
| 56. C2×D3×D8 | C2×C5 | semidirect |
| 57. C2×C3×D16 | C2×C5 | semidirect |
| 58. #5157 | C2×C5 | semidirect |
| 59. C2×#826 | C2×C5 | semidirect |
| 60. #4562 | C2×C5 | semidirect |
| 61. #4509 | C2×C5 | semidirect |
| 62. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 69. C2×C5×D8 | C2×D3 | semidirect |
| 75. C2×C5×C16 | C2×D3 | semidirect |
| 104. C2×C3×D8 | C22×C5 | semidirect |
| 112. C2×C3×C16 | C22×C5 | semidirect |
| 115. #818 | C22×C5 | semidirect |
| 116. C2×C3⋊C16 | C22×C5 | semidirect |
| 132. C5×D8 | #67 | semidirect |
| 143. C2×D16 | C5×D3 | semidirect |
| 161. C2×C5×D3 | D16 | semidirect |
| 178. C3×D8 | C5×D4 | semidirect |
| 185. D24 | C5×D4 | semidirect |
| 219. C2×D8 | C2×C5×D3 | semidirect |
| 225. C2×C16 | C2×C5×D3 | semidirect |
| 291. D8 | C5×#67 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 314. C2×D3 | C5×D16 | semidirect |
| 356. C5 | #71467 | direct (N × H) |
| 375. C3 | C5×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×D8 | 2 |
| C2×C3×C5×D16 | 2 |
| C5×#5157 | 2 |
| C2×C5×#826 | 2 |
| C5×#4562 | 2 |
| C5×#4509 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#2184 | 3 |
| #71467 | 5 |