Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 112 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×C3×C4×C5×D3 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 5. C5×#3722 | C2 | semidirect |
| 16. #63909 | C5 | direct (N × H) |
| 23. C2×C4×C5×D3 | D3 | semidirect |
| 27. C5×C4⋊Dic3 | D3 | semidirect |
| 34. C2×C3×C5×D3 | D4 | semidirect |
| 35. C32×C4×C5 | D4 | semidirect |
| 39. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 40. C2×C3×C4×D3 | C2×C5 | semidirect |
| 41. C2×#626 | C2×C5 | semidirect |
| 42. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 43. #3722 | C2×C5 | semidirect |
| 100. C2×C5×D3 | D12 | semidirect |
| 104. C3×C4×C5 | D12 | semidirect |
| 105. C3×C4×C5 | #67 | semidirect |
| 114. C2×C4×D3 | C5×D3 | semidirect |
| 118. C4⋊Dic3 | C5×D3 | semidirect |
| 119. C32×C5 | #121 | semidirect |
| 134. C2×C3×D3 | C5×D4 | semidirect |
| 135. C32×C4 | C5×D4 | semidirect |
| 181. C4×C5 | #626 | semidirect |
| 193. C3×C5 | #895 | semidirect |
| 194. C3×C5 | #930 | semidirect |
| 212. C2×D3 | C5×D12 | semidirect |
| 216. C3×C4 | C5×D12 | semidirect |
| 217. C3×C4 | C5×#67 | semidirect |
| 225. C32 | C5×#121 | semidirect |
| 248. C5 | #63909 | direct (N × H) |
| 258. C4 | C5×#626 | semidirect |
| 260. C3 | C5×#895 | semidirect |
| 261. C3 | C5×#930 | semidirect |
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×C3×C4×C5×D3 | 2 |
| C2×C5×#626 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C5×#3722 | 2 |
| C5×#930 | 3 |
| C5×#895 | 3 |
| #63909 | 5 |