Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
648 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10617255 | C2 | semidirect |
| 3. #10604944 | C2 | semidirect |
| 4. C2×#64920 | C2 | semidirect |
| 5. #10604472 | C2 | semidirect |
| 6. #10598559 | C2 | semidirect |
| 7. #10598552 | C2 | semidirect |
| 22. C5×#447 | C4 | semidirect |
| 23. #65506 | C4 | semidirect |
| 26. #65322 | C4 | semidirect |
| 29. #65025 | C4 | semidirect |
| 38. C22×C5×D4 | C2×C4 | semidirect |
| 67. C2×C4⋊Dic5 | C2×C4 | semidirect |
| 85. C5×C22⋊C8 | C2×C4 | semidirect |
| 88. C22⋊#168 | C2×C4 | semidirect |
| 153. C22⋊AGL(1,𝔽5) | D8 | semidirect |
| 186. #447 | AGL(1,𝔽5) | semidirect |
| 284. C22×D4 | C2×AGL(1,𝔽5) | semidirect |
| 330. C22⋊C8 | C2×AGL(1,𝔽5) | semidirect |
| 548. C5 | #9277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617255 | 2 |
| #10611737 | 2 |
| #10604944 | 2 |
| C2×#64920 | 2 |
| #10604472 | 2 |
| #10598559 | 2 |
| #10598552 | 2 |
| #9277 | 5 |