Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 294 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×#237 | C2 | semidirect |
| 2. D3×D60 | C2 | semidirect |
| 3. #10623909 | C2 | semidirect |
| 4. C3×#6715 | C2 | semidirect |
| 5. #10623806 | C2 | semidirect |
| 6. #10623801 | C2 | semidirect |
| 7. #10623796 | C2 | semidirect |
| 11. C32×C5×D4 | C22 | semidirect |
| 17. C3×C5×Dic6 | C22 | semidirect |
| 19. C3⋊(C3⋊#168) | C22 | semidirect |
| 20. C3×C3⋊#168 | C22 | semidirect |
| 24. C5×#237 | D3 | semidirect |
| 31. #6715 | D3 | semidirect |
| 46. C3×#237 | D5 | semidirect |
| 58. C3×C5×D4 | C2×D3 | semidirect |
| 59. C3×C5×D4 | C2×D3 | semidirect |
| 70. C5×Dic6 | C2×D3 | semidirect |
| 76. C3⋊#168 | C2×D3 | semidirect |
| 93. C32×D4 | C2×D5 | semidirect |
| 99. C3×Dic6 | C2×D5 | semidirect |
| 123. #237 | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 141. C5×D4 | D32 | semidirect |
| 177. C3×D4 | D3×D5 | semidirect |
| 178. C3×D4 | C2×D15 | semidirect |
| 190. Dic6 | C2×D15 | semidirect |
| 217. C3×C5 | #911 | semidirect |
| 218. C3×C5 | #949 | semidirect |
| 243. C32 | #4095 | semidirect |
| 250. D4 | D3×D15 | semidirect |
| 268. C5 | #63925 | semidirect |
| 278. C3 | #91480 | semidirect |
| 279. C3 | #91838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#237 | 2 |
| D3×D60 | 2 |
| #10623909 | 2 |
| C3×#6715 | 2 |
| #10623806 | 2 |
| #10623801 | 2 |
| #10623796 | 2 |
| #91838 | 3 |
| #91480 | 3 |
| #63925 | 5 |