Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10624205 | C2 | semidirect |
| 2. #10624194 | C2 | semidirect |
| 3. #10623899 | C2 | semidirect |
| 4. C3×D120 | C2 | semidirect |
| 5. C3×C5×#204 | C2 | semidirect |
| 6. #10623801 | C2 | semidirect |
| 7. #10623798 | C2 | semidirect |
| 13. C3×D60 | C22 | semidirect |
| 15. C3×C5×Dic6 | C22 | semidirect |
| 19. C32×C5×C8 | C22 | semidirect |
| 20. C3⋊(C3⋊#168) | C22 | semidirect |
| 29. D120 | D3 | semidirect |
| 33. C5×#204 | D3 | semidirect |
| 50. C3×#204 | D5 | semidirect |
| 60. D60 | C2×D3 | semidirect |
| 66. C5×Dic6 | C2×D3 | semidirect |
| 73. C3×C5×C8 | C2×D3 | semidirect |
| 74. C3×C5×C8 | C2×D3 | semidirect |
| 97. C3×Dic6 | C2×D5 | semidirect |
| 101. C32×C8 | C2×D5 | semidirect |
| 133. #204 | D15 | semidirect |
| 137. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 147. C5×C8 | D32 | semidirect |
| 188. Dic6 | C2×D15 | semidirect |
| 190. C3×C8 | D3×D5 | semidirect |
| 191. C3×C8 | C2×D15 | semidirect |
| 216. C3×C5 | #911 | semidirect |
| 217. C3×C5 | #914 | semidirect |
| 242. C32 | #4060 | semidirect |
| 253. C8 | D3×D15 | semidirect |
| 266. C5 | #63798 | semidirect |
| 276. C3 | #91258 | semidirect |
| 277. C3 | #91803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624205 | 2 |
| #10624194 | 2 |
| #10623899 | 2 |
| C3×D120 | 2 |
| C3×C5×#204 | 2 |
| #10623801 | 2 |
| #10623798 | 2 |
| #91803 | 3 |
| #91258 | 3 |
| #63798 | 5 |