Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
402 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 96 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×C3×C4×D15 | C2 | semidirect |
| 3. C2×D3×Dic15 | C2 | semidirect |
| 4. #10623906 | C2 | semidirect |
| 5. C3×C5×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #10623811 | C2 | semidirect |
| 7. Dic3×Dic15 | C2 | semidirect |
| 18. #67150 | C4 | semidirect |
| 23. C2×C4×D15 | D3 | semidirect |
| 33. C5×(C2×D3)⋊C4 | D3 | semidirect |
| 39. C2×C3×D15 | C2×C4 | semidirect |
| 42. C2×C3×C5×D3 | C2×C4 | semidirect |
| 45. C3⋊Dic15 | C2×C4 | semidirect |
| 46. C3×Dic15 | D4 | semidirect |
| 53. C3×(C2×D3)⋊C4 | D5 | semidirect |
| 111. C2×D15 | C4×D3 | semidirect |
| 114. C2×C5×D3 | C4×D3 | semidirect |
| 128. Dic15 | #67 | semidirect |
| 140. (C2×D3)⋊C4 | D15 | semidirect |
| 146. C32×C5 | C4×D4 | semidirect |
| 163. C2×C3×D3 | C4×D5 | semidirect |
| 231. C3×C5 | #67⋊C4 | semidirect |
| 232. C3×C5 | C4×#67 | semidirect |
| 247. C2×D3 | C4×D15 | semidirect |
| 266. C32 | #4027 | semidirect |
| 290. C5 | #63879 | semidirect |
| 304. C3 | #91440 | semidirect |
| 305. C3 | #91770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D15 | 2 |
| C2×#67150 | 2 |
| C2×D3×Dic15 | 2 |
| #10623906 | 2 |
| C3×C5×(C2×D3)⋊C4 | 2 |
| #10623811 | 2 |
| Dic3×Dic15 | 2 |
| #91770 | 3 |
| #91440 | 3 |
| #63879 | 5 |