Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 2. C2×C3⋊D3×Dic5 | C2 | semidirect |
| 3. C2×D5×C3⋊Dic3 | C2 | semidirect |
| 4. C4×C3⋊Dic15 | C2 | semidirect |
| 5. C5×#3752 | C2 | semidirect |
| 6. C32×#685 | C2 | semidirect |
| 7. #10623774 | C2 | semidirect |
| 16. #67138 | C4 | semidirect |
| 25. C3×#685 | D3 | semidirect |
| 30. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 33. C2×C32×D5 | C2×C4 | semidirect |
| 35. C3⋊Dic15 | C2×C4 | semidirect |
| 36. C3⋊Dic15 | D4 | semidirect |
| 44. #3752 | D5 | semidirect |
| 67. #685 | C3⋊D3 | semidirect |
| 86. C2×C3×D5 | C4×D3 | semidirect |
| 99. C32×C5 | C4×D4 | semidirect |
| 116. C2×C3⋊D3 | C4×D5 | semidirect |
| 144. C2×D5 | C4×C3⋊D3 | semidirect |
| 162. C3×C5 | #67⋊C4 | semidirect |
| 180. C32 | #4027 | semidirect |
| 196. C5 | #64090 | semidirect |
| 209. C3 | #91442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67138 | 2 |
| C2×C3⋊D3×Dic5 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| C4×C3⋊Dic15 | 2 |
| C5×#3752 | 2 |
| C32×#685 | 2 |
| #10623774 | 2 |
| #91442 | 3 |
| #64090 | 5 |