Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 154 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×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C32×C5×C8 | C2 | semidirect |
| 3. C5×#3745 | C2 | direct (N × H) |
| 8. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 9. C32×C5×C8 | C22 | semidirect |
| 10. C2×#3745 | C5 | direct (N × H) |
| 12. C2×C3×C5×C8 | D3 | semidirect |
| 20. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 21. C2×C32×C8 | C2×C5 | semidirect |
| 22. #3745 | C2×C5 | direct (N × H) |
| 27. C3×C5×C8 | C2×D3 | semidirect |
| 29. C2×C32×C5 | D8 | semidirect |
| 34. C2×C5×C8 | C3⋊D3 | semidirect |
| 38. C4⋊(C3⋊D3) | C22×C5 | semidirect |
| 39. C32×C8 | C22×C5 | semidirect |
| 46. C2×C3×C8 | C5×D3 | semidirect |
| 48. C32×C5 | C2×D8 | semidirect |
| 53. C5×C8 | C2×C3⋊D3 | semidirect |
| 60. C2×C3×C5 | D24 | semidirect |
| 67. C3×C8 | C2×C5×D3 | semidirect |
| 73. C2×C32 | C5×D8 | semidirect |
| 78. C2×C8 | C5×C3⋊D3 | semidirect |
| 79. C3×C5 | C2×D24 | semidirect |
| 86. C2×C5 | #3745 | direct (N × H) |
| 88. C32 | C2×C5×D8 | semidirect |
| 93. C8 | C2×C5×C3⋊D3 | semidirect |
| 94. C2×C3 | C5×D24 | semidirect |
| 97. C5 | C2×#3745 | direct (N × H) |
| 103. C3 | C2×C5×D24 | semidirect |
| 105. C2 | C5×#3745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C32×C5×C8 | 2 |
| C5×#3745 | 2 |
| C2×C5×D24 | 3 |
| C2×#3745 | 5 |