Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 3. C2×#67155 | C2 | semidirect |
| 4. C3×#6714 | C2 | semidirect |
| 5. #10623829 | C2 | semidirect |
| 11. C2×(C3⋊D3)⋊D5 | C4 | semidirect |
| 12. C2×C32×C4×C5 | C22 | semidirect |
| 13. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 15. C2×C3×Dic15 | C22 | semidirect |
| 22. #6714 | D3 | semidirect |
| 32. C2×C3×D15 | C2×C4 | semidirect |
| 39. C2×C4×C3⋊D3 | D5 | semidirect |
| 51. C2×C3×C4×C5 | C2×D3 | semidirect |
| 52. C2×Dic15 | C2×D3 | semidirect |
| 63. C5×C3⋊D3 | C22⋊C4 | semidirect |
| 75. C2×C32×C4 | C2×D5 | semidirect |
| 76. C2×C3⋊Dic3 | C2×D5 | semidirect |
| 84. C2×D15 | C4×D3 | semidirect |
| 109. C32×C5 | C2×C22⋊C4 | semidirect |
| 117. C2×C4×C5 | D32 | semidirect |
| 151. C2×C3×C4 | D3×D5 | semidirect |
| 172. C3⋊D3 | #685 | semidirect |
| 180. C3×C5 | D3×C22⋊C4 | semidirect |
| 207. C32 | C2×#685 | semidirect |
| 217. C2×C4 | (C3⋊D3)⋊D5 | semidirect |
| 228. C5 | #63921 | semidirect |
| 241. C3 | D3×#685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊D5 | 2 |
| C2×C4×C5×C3⋊D3 | 2 |
| C2×#67155 | 2 |
| C3×#6714 | 2 |
| #10623829 | 2 |
| D3×#685 | 3 |
| #63921 | 5 |