Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 158 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×C32×C5×D4 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C5×#638 | C2 | semidirect |
| 4. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 5. C5×#3757 | C2 | semidirect |
| 6. C5×#3752 | C2 | semidirect |
| 7. C5×#3750 | C2 | semidirect |
| 20. #64148 | C5 | direct (N × H) |
| 21. C2×C3×C5×D4 | D3 | semidirect |
| 33. C22×C32×C5 | D4 | semidirect |
| 41. C5×C3⋊Dic3 | D4 | semidirect |
| 43. C2×C32×D4 | C2×C5 | semidirect |
| 44. C2×#638 | C2×C5 | semidirect |
| 45. C2×#638 | C2×C5 | semidirect |
| 46. C22×C3⋊Dic3 | C2×C5 | semidirect |
| 47. #3757 | C2×C5 | semidirect |
| 48. #3752 | C2×C5 | semidirect |
| 49. #3750 | C2×C5 | semidirect |
| 70. C2×C5×D4 | C3⋊D3 | semidirect |
| 91. C22×C3×C5 | #67 | semidirect |
| 100. C2×C3×D4 | C5×D3 | semidirect |
| 107. C32×C5 | #121 | semidirect |
| 124. C22×C32 | C5×D4 | semidirect |
| 132. C3⋊Dic3 | C5×D4 | semidirect |
| 159. C22×C5 | #638 | semidirect |
| 173. C2×D4 | C5×C3⋊D3 | semidirect |
| 178. C3×C5 | #939 | semidirect |
| 184. C22×C3 | C5×#67 | semidirect |
| 199. C32 | C5×#121 | semidirect |
| 217. C5 | #64148 | direct (N × H) |
| 226. C22 | C5×#638 | semidirect |
| 232. C3 | C5×#939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| C2×C5×#638 | 2 |
| C22×C5×C3⋊Dic3 | 2 |
| C5×#3757 | 2 |
| C5×#3752 | 2 |
| C5×#3750 | 2 |
| C5×#939 | 3 |
| #64148 | 5 |