Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 74 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×C4⋊(C3⋊D15) | C2 | semidirect |
| 2. C3×C5×#235 | C2 | semidirect |
| 3. C3×#6710 | C2 | semidirect |
| 4. #10623806 | C2 | semidirect |
| 5. #10623800 | C2 | semidirect |
| 13. C3×C5×D12 | C22 | semidirect |
| 15. C3×C5×Dic6 | C22 | semidirect |
| 16. C3×C3⋊#168 | C22 | semidirect |
| 22. C5×#235 | D3 | semidirect |
| 25. #6710 | D3 | semidirect |
| 38. C3×#235 | D5 | semidirect |
| 59. C5×D12 | C2×D3 | semidirect |
| 61. C5×Dic6 | C2×D3 | semidirect |
| 62. C3⋊#168 | C2×D3 | semidirect |
| 80. C3×D12 | C2×D5 | semidirect |
| 82. C3×Dic6 | C2×D5 | semidirect |
| 104. #235 | D15 | semidirect |
| 114. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 160. D12 | C2×D15 | semidirect |
| 162. Dic6 | C2×D15 | semidirect |
| 182. C3×C5 | #908 | semidirect |
| 183. C3×C5 | #949 | semidirect |
| 207. C32 | #4095 | semidirect |
| 228. C5 | #63825 | semidirect |
| 237. C3 | #91305 | semidirect |
| 238. C3 | #91838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D15) | 2 |
| C3×C5×#235 | 2 |
| C3×#6710 | 2 |
| #10623806 | 2 |
| #10623800 | 2 |
| #91838 | 3 |
| #91305 | 3 |
| #63825 | 5 |