Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 63 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. C5×D4×C3⋊D3 | C2 | semidirect |
| 2. #10624227 | C2 | semidirect |
| 3. C3×#6715 | C2 | semidirect |
| 4. #10623821 | C2 | semidirect |
| 5. #10623818 | C2 | semidirect |
| 9. C32×C5×D4 | C22 | semidirect |
| 11. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C3×D60 | C22 | semidirect |
| 15. C3×C3⋊#168 | C22 | semidirect |
| 20. #6715 | D3 | semidirect |
| 34. D4×C3⋊D3 | D5 | semidirect |
| 43. C3×C5×D4 | C2×D3 | semidirect |
| 44. D60 | C2×D3 | semidirect |
| 53. C3⋊#168 | C2×D3 | semidirect |
| 59. C5×C3⋊D3 | D8 | semidirect |
| 68. C32×D4 | C2×D5 | semidirect |
| 70. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 98. C32×C5 | C2×D8 | semidirect |
| 103. C5×D4 | D32 | semidirect |
| 132. C3×D4 | D3×D5 | semidirect |
| 154. C3⋊D3 | #686 | semidirect |
| 162. C3×C5 | D3×D8 | semidirect |
| 183. C32 | C2×#686 | semidirect |
| 190. D4 | (C3⋊D3)⋊D5 | semidirect |
| 203. C5 | #63926 | semidirect |
| 213. C3 | D3×#686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×C3⋊D3 | 2 |
| #10624227 | 2 |
| C3×#6715 | 2 |
| #10623821 | 2 |
| #10623818 | 2 |
| D3×#686 | 3 |
| #63926 | 5 |