Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
512 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 114 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. C3×C5×#467 | C2 | semidirect |
| 3. C2×C5×#828 | C2 | semidirect |
| 4. C5×#4549 | C2 | semidirect |
| 5. C5×#4491 | C2 | semidirect |
| 8. C2×C3×C5×Q16 | C22 | semidirect |
| 14. C3×C5×#107 | C22 | semidirect |
| 17. C2×C5×C3⋊C16 | C22 | semidirect |
| 18. #71085 | C5 | direct (N × H) |
| 21. C5×#467 | D3 | semidirect |
| 43. C3×#467 | C2×C5 | semidirect |
| 44. C2×#828 | C2×C5 | semidirect |
| 45. #4549 | C2×C5 | semidirect |
| 46. #4491 | C2×C5 | semidirect |
| 48. C2×C5×Q16 | C2×D3 | semidirect |
| 56. C5×#107 | C2×D3 | semidirect |
| 78. C2×C3×Q16 | C22×C5 | semidirect |
| 84. C3×#107 | C22×C5 | semidirect |
| 87. C2×C3⋊C16 | C22×C5 | semidirect |
| 108. #467 | C5×D3 | semidirect |
| 113. C22×C3×C5 | SD32 | semidirect |
| 161. C2×Q16 | C2×C5×D3 | semidirect |
| 169. #107 | C2×C5×D3 | semidirect |
| 200. C22×C5 | #828 | semidirect |
| 225. C3×C5 | #2187 | semidirect |
| 228. C22×C3 | C5×SD32 | semidirect |
| 267. C5 | #71085 | direct (N × H) |
| 274. C22 | C5×#828 | semidirect |
| 281. C3 | C5×#2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D24 | 2 |
| C3×C5×#467 | 2 |
| C2×C5×#828 | 2 |
| C5×#4549 | 2 |
| C5×#4491 | 2 |
| C5×#2187 | 3 |
| #71085 | 5 |