Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
3678 conjugacy classes of subgroups; only the 1219 normal subgroups are shown.
This group has 3678 conjugacy classes of subgroups — too many to draw. Only its 1219 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×#383 | C2 | semidirect |
| 3. C2×#65226 | C2 | semidirect |
| 4. D5×#383 | C2 | direct (N × H) |
| 6. C2×#64940 | C2 | semidirect |
| 11. C2×C42×D5 | C4 | semidirect |
| 13. C5×#383 | C22 | semidirect |
| 17. #65226 | C22 | semidirect |
| 19. #64940 | C22 | semidirect |
| 31. C2×C42×C5 | C2×C4 | semidirect |
| 33. C2×C4×Dic5 | C2×C4 | semidirect |
| 35. C42×D5 | C2×C4 | semidirect |
| 43. C2×#383 | D5 | direct (N × H) |
| 64. C42×C5 | C22×C4 | semidirect |
| 65. C4×Dic5 | C22×C4 | semidirect |
| 74. #383 | C2×D5 | direct (N × H) |
| 111. C2×C42 | C4×D5 | semidirect |
| 120. C2×D5 | #383 | direct (N × H) |
| 147. C42 | C2×C4×D5 | semidirect |
| 148. C2×C5 | C2×#383 | semidirect |
| 151. D5 | C2×#383 | direct (N × H) |
| 171. C5 | C22×#383 | semidirect |
| 184. C2 | D5×#383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×D5 | 2 |
| C2×C5×#383 | 2 |
| C2×#65226 | 2 |
| D5×#383 | 2 |
| C2×D5×#95 | 2 |
| C2×#64940 | 2 |
| C22×#383 | 5 |