Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×C3×Dic30 | C2 | semidirect |
| 3. C2×C3×C5×D12 | C2 | semidirect |
| 4. C2×#67152 | C2 | semidirect |
| 5. C2×D3×Dic15 | C2 | semidirect |
| 6. #10624196 | C2 | direct (N × H) |
| 13. C4×C3⋊D15 | C22 | semidirect |
| 15. C3×Dic30 | C22 | semidirect |
| 16. C3×C5×D12 | C22 | semidirect |
| 17. #67152 | C22 | semidirect |
| 18. D3×Dic15 | C22 | semidirect |
| 27. C2×Dic30 | D3 | semidirect |
| 28. C2×C5×D12 | D3 | semidirect |
| 43. C2×C3×D12 | D5 | semidirect |
| 66. Dic30 | C2×D3 | semidirect |
| 67. C5×D12 | C2×D3 | semidirect |
| 74. C2×C32×C5 | #41 | semidirect |
| 90. C3×D12 | C2×D5 | semidirect |
| 122. C2×D12 | D15 | semidirect |
| 128. C32×C5 | C2×#41 | semidirect |
| 151. C2×C3×C5 | #237 | semidirect |
| 152. C2×C3×C5 | #239 | semidirect |
| 177. D12 | C2×D15 | semidirect |
| 191. C2×C32 | #711 | semidirect |
| 202. C3×C5 | C2×#237 | semidirect |
| 203. C3×C5 | C2×#239 | semidirect |
| 226. C2×C5 | #3796 | semidirect |
| 229. C32 | C2×#711 | semidirect |
| 243. C2×C3 | #6768 | semidirect |
| 244. C2×C3 | #6819 | semidirect |
| 251. C5 | C2×#3796 | semidirect |
| 261. C3 | C2×#6768 | semidirect |
| 262. C3 | C2×#6819 | semidirect |
| 265. C2 | #10624196 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D15 | 2 |
| C2×C3×Dic30 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×#67152 | 2 |
| C2×D3×Dic15 | 2 |
| #10624196 | 2 |
| C2×#6819 | 3 |
| C2×#6768 | 3 |
| C2×#3796 | 5 |