Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 452 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×Q16 | C2 | semidirect |
| 2. C2×C3×C5×SD32 | C2 | semidirect |
| 4. C2×C5×#827 | C2 | semidirect |
| 5. C5×#4564 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C5×#4503 | C2 | semidirect |
| 24. #71483 | C5 | direct (N × H) |
| 27. C2×C5×SD32 | D3 | semidirect |
| 42. C3×C5×Q16 | D4 | semidirect |
| 51. C5×Dic12 | D4 | semidirect |
| 56. C2×D3×Q16 | C2×C5 | semidirect |
| 57. C2×C3×SD32 | C2×C5 | semidirect |
| 59. C2×#827 | C2×C5 | semidirect |
| 60. #4564 | C2×C5 | semidirect |
| 61. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 62. #4503 | C2×C5 | semidirect |
| 128. C5×Q16 | #67 | semidirect |
| 141. C2×SD32 | C5×D3 | semidirect |
| 152. C2×C5×D3 | SD32 | semidirect |
| 169. C3×Q16 | C5×D4 | semidirect |
| 178. Dic12 | C5×D4 | semidirect |
| 271. Q16 | C5×#67 | semidirect |
| 282. C3×C5 | #2185 | semidirect |
| 289. C2×D3 | C5×SD32 | semidirect |
| 327. C5 | #71483 | direct (N × H) |
| 341. C3 | C5×#2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×Q16 | 2 |
| C2×C3×C5×SD32 | 2 |
| C5×#5157 | 2 |
| C2×C5×#827 | 2 |
| C5×#4564 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#4503 | 2 |
| C5×#2185 | 3 |
| #71483 | 5 |