Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 128 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×C5×#624 | C2 | semidirect |
| 3. C3×C5×C4⋊Dic3 | C2 | semidirect |
| 4. C3×C4×C5×Dic3 | C2 | semidirect |
| 5. C5×#3722 | C2 | semidirect |
| 10. C5×C4⋊(C3⋊D3) | C4 | semidirect |
| 15. #63894 | C5 | direct (N × H) |
| 25. C5×C4⋊Dic3 | D3 | semidirect |
| 26. C4×C5×Dic3 | D3 | semidirect |
| 30. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 31. C32×C4×C5 | C2×C4 | semidirect |
| 34. C3×C5×Dic3 | D4 | semidirect |
| 37. C2×#624 | C2×C5 | semidirect |
| 38. C3×C4⋊Dic3 | C2×C5 | semidirect |
| 39. C3×C4×Dic3 | C2×C5 | semidirect |
| 40. #3722 | C2×C5 | semidirect |
| 71. C4⋊(C3⋊D3) | C4×C5 | semidirect |
| 92. C3×C4×C5 | C4×D3 | semidirect |
| 93. C3×C4×C5 | C4×D3 | semidirect |
| 96. C5×Dic3 | D12 | semidirect |
| 106. C4⋊Dic3 | C5×D3 | semidirect |
| 107. C4×Dic3 | C5×D3 | semidirect |
| 108. C32×C5 | C4×D4 | semidirect |
| 119. C2×C3⋊D3 | C2×C4×C5 | semidirect |
| 120. C32×C4 | C2×C4×C5 | semidirect |
| 123. C3×Dic3 | C5×D4 | semidirect |
| 161. C4×C5 | #624 | semidirect |
| 172. C3×C5 | C4×D12 | semidirect |
| 173. C3×C5 | #893 | semidirect |
| 190. C3×C4 | C4×C5×D3 | semidirect |
| 191. C3×C4 | C4×C5×D3 | semidirect |
| 194. Dic3 | C5×D12 | semidirect |
| 199. C32 | C4×C5×D4 | semidirect |
| 219. C5 | #63894 | direct (N × H) |
| 227. C4 | C5×#624 | semidirect |
| 229. C3 | C4×C5×D12 | semidirect |
| 230. C3 | C5×#893 | 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×C5×#624 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| C3×C4×C5×Dic3 | 2 |
| C5×#3722 | 2 |
| C5×#893 | 3 |
| C4×C5×D12 | 3 |
| #63894 | 5 |