Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×C5×#239 | C2 | semidirect |
| 2. D3×D60 | C2 | semidirect |
| 3. #10623911 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623800 | C2 | semidirect |
| 6. #10623798 | C2 | semidirect |
| 7. #10623796 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 15. C3×C5×D12 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 24. C5×#239 | D3 | semidirect |
| 29. #6717 | D3 | semidirect |
| 46. C3×#239 | D5 | semidirect |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 68. C5×D12 | C2×D3 | semidirect |
| 76. C3⋊#168 | C2×D3 | semidirect |
| 93. C32×Q8 | C2×D5 | semidirect |
| 97. C3×D12 | C2×D5 | semidirect |
| 123. #239 | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 139. C5×Q8 | D32 | semidirect |
| 173. C3×Q8 | D3×D5 | semidirect |
| 174. C3×Q8 | C2×D15 | semidirect |
| 187. D12 | C2×D15 | semidirect |
| 216. C3×C5 | #914 | semidirect |
| 217. C3×C5 | #949 | semidirect |
| 242. C32 | #4095 | semidirect |
| 244. Q8 | D3×D15 | semidirect |
| 266. C5 | #63939 | semidirect |
| 276. C3 | #91504 | semidirect |
| 277. C3 | #91838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#239 | 2 |
| D3×D60 | 2 |
| #10623911 | 2 |
| C3×#6717 | 2 |
| #10623800 | 2 |
| #10623798 | 2 |
| #10623796 | 2 |
| #91838 | 3 |
| #91504 | 3 |
| #63939 | 5 |