Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1398 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1398 conjugacy classes of subgroups — too many to draw. Only its 244 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×#65731 | C2 | semidirect |
| 2. AGL(1,𝔽5)×#127 | C2 | semidirect |
| 4. #10604803 | C2 | semidirect |
| 5. #10604616 | C2 | semidirect |
| 6. #10603847 | C2 | semidirect |
| 7. C4×#3992 | C2 | semidirect |
| 22. C5×#493 | C4 | semidirect |
| 23. #65440 | C4 | semidirect |
| 24. #65362 | C4 | semidirect |
| 25. #64984 | C4 | semidirect |
| 41. C2×C5×D8 | C2×C4 | semidirect |
| 42. C5×#127 | C2×C4 | semidirect |
| 44. #4086 | C2×C4 | semidirect |
| 45. C2×#686 | C2×C4 | semidirect |
| 48. C2×D40 | C2×C4 | semidirect |
| 50. #4020 | C2×C4 | semidirect |
| 56. #3992 | D4 | semidirect |
| 57. C4×C5×C8 | C2×C4 | semidirect |
| 58. C8×Dic5 | C2×C4 | semidirect |
| 59. C4×#168 | C2×C4 | semidirect |
| 112. #493 | AGL(1,𝔽5) | semidirect |
| 152. C5×C8 | C4×D4 | semidirect |
| 153. #168 | C4×D4 | semidirect |
| 161. C2×D8 | C2×AGL(1,𝔽5) | semidirect |
| 167. #127 | C2×AGL(1,𝔽5) | semidirect |
| 185. C4×C8 | C2×AGL(1,𝔽5) | semidirect |
| 200. C4×C5 | #442 | semidirect |
| 202. Dic5 | #442 | semidirect |
| 277. C8 | D4×AGL(1,𝔽5) | semidirect |
| 278. C5 | #21690 | semidirect |
| 295. C4 | #65731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65731 | 2 |
| AGL(1,𝔽5)×#127 | 2 |
| D5×#493 | 2 |
| #10604803 | 2 |
| #10604616 | 2 |
| #10603847 | 2 |
| C4×#3992 | 2 |
| #21690 | 5 |