Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
662 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 244 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. C5×Q8×C3⋊D3 | C2 | semidirect |
| 2. C3×C5×D3×Q8 | C2 | semidirect |
| 4. C5×#3797 | C2 | semidirect |
| 5. C5×D3×Dic6 | C2 | semidirect |
| 8. C32×C5×Q8 | C22 | semidirect |
| 10. C5×#634 | C22 | semidirect |
| 12. C3×C5×Dic6 | C22 | semidirect |
| 13. C5×#627 | C22 | semidirect |
| 16. D32×Q8 | C5 | direct (N × H) |
| 22. C5×D3×Q8 | D3 | direct (N × H) |
| 27. C5×D32 | Q8 | direct (N × H) |
| 32. Q8×C3⋊D3 | C2×C5 | semidirect |
| 33. C3×D3×Q8 | C2×C5 | semidirect |
| 35. #3797 | C2×C5 | semidirect |
| 36. D3×Dic6 | C2×C5 | semidirect |
| 40. C3×C5×Q8 | C2×D3 | semidirect |
| 51. C5×Dic6 | C2×D3 | semidirect |
| 54. C5×C3⋊D3 | C2×Q8 | semidirect |
| 55. C3×C5×D3 | C2×Q8 | semidirect |
| 62. C32×Q8 | C22×C5 | semidirect |
| 64. #634 | C22×C5 | semidirect |
| 66. C3×Dic6 | C22×C5 | semidirect |
| 67. #627 | C22×C5 | semidirect |
| 86. D3×Q8 | C5×D3 | direct (N × H) |
| 89. C32×C5 | C22×Q8 | semidirect |
| 94. C5×Q8 | D32 | direct (N × H) |
| 101. D32 | C5×Q8 | direct (N × H) |
| 111. C5×D3 | D3×Q8 | direct (N × H) |
| 115. C3×Q8 | C2×C5×D3 | semidirect |
| 126. Dic6 | C2×C5×D3 | semidirect |
| 134. C3⋊D3 | C2×C5×Q8 | semidirect |
| 135. C3×D3 | C2×C5×Q8 | semidirect |
| 142. C3×C5 | C2×D3×Q8 | semidirect |
| 157. C32 | C22×C5×Q8 | semidirect |
| 162. Q8 | C5×D32 | direct (N × H) |
| 172. D3 | C5×D3×Q8 | direct (N × H) |
| 173. C5 | D32×Q8 | direct (N × H) |
| 181. C3 | C2×C5×D3×Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C3×C5×D3×Q8 | 2 |
| C4×C5×D32 | 2 |
| C5×#3797 | 2 |
| C5×D3×Dic6 | 2 |
| C2×C5×D3×Q8 | 3 |
| D32×Q8 | 5 |