Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 159 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×C4×C5×C3⋊D3 | C2 | semidirect |
| 2. C2×C3×C4×D15 | C2 | semidirect |
| 3. C2×#67158 | C2 | semidirect |
| 4. C2×#67157 | C2 | semidirect |
| 5. C2×#67156 | C2 | semidirect |
| 6. #10624223 | C2 | direct (N × H) |
| 12. C4×C5×C3⋊D3 | C22 | semidirect |
| 14. C3×C4×D15 | C22 | semidirect |
| 15. #67158 | C22 | semidirect |
| 16. #67157 | C22 | semidirect |
| 17. #67156 | C22 | semidirect |
| 19. C2×C4×D15 | D3 | semidirect |
| 37. C2×C4×C3⋊D3 | D5 | semidirect |
| 50. C4×D15 | C2×D3 | semidirect |
| 62. C2×C32×C5 | #41 | semidirect |
| 76. C4×C3⋊D3 | C2×D5 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 129. C2×C3×C5 | #235 | semidirect |
| 161. C2×C32 | #709 | semidirect |
| 172. C3×C5 | C2×#235 | semidirect |
| 190. C2×C5 | #3798 | semidirect |
| 193. C32 | C2×#709 | semidirect |
| 207. C2×C3 | #6771 | semidirect |
| 212. C5 | C2×#3798 | semidirect |
| 222. C3 | C2×#6771 | semidirect |
| 225. C2 | #10624223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3×C4×D15 | 2 |
| C2×#67158 | 2 |
| C2×#67157 | 2 |
| C2×#67156 | 2 |
| #10624223 | 2 |
| C2×#6771 | 3 |
| C2×#3798 | 5 |