Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| 3. C2×#67154 | C2 | semidirect |
| 4. C3×#6714 | C2 | semidirect |
| 5. C3×#6712 | C2 | semidirect |
| 6. #10623830 | C2 | semidirect |
| 7. #10623828 | C2 | semidirect |
| 18. #67156 | C4 | semidirect |
| 28. #6714 | D3 | semidirect |
| 29. #6712 | D3 | semidirect |
| 39. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 42. C2×C3×D15 | C2×C4 | semidirect |
| 44. C5×C3⋊Dic3 | D4 | semidirect |
| 47. C3×Dic15 | C2×C4 | semidirect |
| 49. C2×C4×C3⋊D3 | D5 | semidirect |
| 109. C2×D15 | C4×D3 | semidirect |
| 127. Dic15 | C4×D3 | semidirect |
| 149. C32×C5 | C4×D4 | semidirect |
| 163. C2×C3⋊D3 | C4×D5 | semidirect |
| 168. C3⋊Dic3 | C22⋊D5 | semidirect |
| 236. C3×C5 | #67⋊C4 | semidirect |
| 237. C3×C5 | #893 | semidirect |
| 273. C32 | C4×C22⋊D5 | semidirect |
| 298. C5 | #63881 | semidirect |
| 312. C3 | #91441 | semidirect |
| 313. C3 | #91446 | semidirect |
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×#67156 | 2 |
| C2×#67154 | 2 |
| C3×#6714 | 2 |
| C3×#6712 | 2 |
| #10623830 | 2 |
| #10623828 | 2 |
| #91446 | 3 |
| #91441 | 3 |
| #63881 | 5 |