Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. C2×C3×C5×SD32 | C2 | semidirect |
| 3. C5×#5188 | C2 | semidirect |
| 4. C2×C5×#828 | C2 | semidirect |
| 5. C5×#4562 | C2 | semidirect |
| 6. C5×#4509 | C2 | semidirect |
| 7. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 10. C2×C3×C5×Q16 | C22 | semidirect |
| 19. C2×C3×C5×C16 | C22 | semidirect |
| 22. C5×#818 | C22 | semidirect |
| 23. C2×C5×C3⋊C16 | C22 | semidirect |
| 24. #71485 | C5 | direct (N × H) |
| 27. C2×C5×SD32 | D3 | semidirect |
| 57. C2×C3×SD32 | C2×C5 | semidirect |
| 58. #5188 | C2×C5 | semidirect |
| 59. C2×#828 | C2×C5 | semidirect |
| 60. #4562 | C2×C5 | semidirect |
| 61. #4509 | C2×C5 | semidirect |
| 62. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 64. C2×C5×Q16 | C2×D3 | semidirect |
| 75. C2×C5×C16 | C2×D3 | semidirect |
| 102. C2×C3×Q16 | C22×C5 | semidirect |
| 111. C2×C3×C16 | C22×C5 | semidirect |
| 114. #818 | C22×C5 | semidirect |
| 115. C2×C3⋊C16 | C22×C5 | semidirect |
| 142. C2×SD32 | C5×D3 | semidirect |
| 157. C2×C5×D3 | SD32 | semidirect |
| 210. C2×Q16 | C2×C5×D3 | semidirect |
| 221. C2×C16 | C2×C5×D3 | semidirect |
| 292. C3×C5 | #2187 | semidirect |
| 303. C2×D3 | C5×SD32 | semidirect |
| 343. C5 | #71485 | direct (N × H) |
| 360. C3 | C5×#2187 | 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×SD32 | 2 |
| C5×#5188 | 2 |
| C2×C5×#828 | 2 |
| C5×#4562 | 2 |
| C5×#4509 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#2187 | 3 |
| #71485 | 5 |