Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 232 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. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#627 | C2 | semidirect |
| 4. C2×C5×#625 | C2 | semidirect |
| 5. C5×#3805 | C2 | direct (N × H) |
| 6. C2×C5×D3×Dic3 | C2 | semidirect |
| 12. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 13. C3×C5×#67 | C22 | semidirect |
| 15. C5×#627 | C22 | semidirect |
| 16. C5×#625 | C22 | semidirect |
| 17. C5×D3×Dic3 | C22 | semidirect |
| 18. C2×#3805 | C5 | direct (N × H) |
| 21. C2×C5×#67 | D3 | semidirect |
| 37. C22×C3⋊Dic3 | C2×C5 | semidirect |
| 38. C2×C3×#67 | C2×C5 | semidirect |
| 39. C2×#627 | C2×C5 | semidirect |
| 40. C2×#625 | C2×C5 | semidirect |
| 41. #3805 | C2×C5 | direct (N × H) |
| 42. C2×D3×Dic3 | C2×C5 | semidirect |
| 50. C5×#67 | C2×D3 | semidirect |
| 63. C2×C32×C5 | #41 | semidirect |
| 76. C2×C3⋊Dic3 | C22×C5 | semidirect |
| 77. C3×#67 | C22×C5 | semidirect |
| 79. #627 | C22×C5 | semidirect |
| 80. #625 | C22×C5 | semidirect |
| 81. D3×Dic3 | C22×C5 | semidirect |
| 100. C2×#67 | C5×D3 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 132. C2×C3×C5 | #237 | semidirect |
| 142. #67 | C2×C5×D3 | semidirect |
| 162. C2×C32 | C5×#41 | semidirect |
| 172. C3×C5 | C2×#237 | semidirect |
| 191. C2×C5 | #3805 | direct (N × H) |
| 193. C32 | C2×C5×#41 | semidirect |
| 209. C2×C3 | C5×#237 | semidirect |
| 212. C5 | C2×#3805 | direct (N × H) |
| 222. C3 | C2×C5×#237 | semidirect |
| 225. C2 | C5×#3805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#627 | 2 |
| C2×C5×#625 | 2 |
| C5×#3805 | 2 |
| C2×C5×D3×Dic3 | 2 |
| C2×C5×#237 | 3 |
| C2×#3805 | 5 |