Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
578 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 94 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. D4×#700 | C2 | semidirect |
| 3. #10604678 | C2 | semidirect |
| 4. #10604650 | C2 | semidirect |
| 5. C4×#4007 | C2 | semidirect |
| 6. #10598594 | C2 | semidirect |
| 7. #10598588 | C2 | semidirect |
| 22. C5×#474 | C4 | semidirect |
| 23. #65376 | C4 | semidirect |
| 24. #65304 | C4 | semidirect |
| 27. #65132 | C4 | semidirect |
| 138. #700 | D8 | semidirect |
| 165. #474 | AGL(1,𝔽5) | semidirect |
| 199. C5×D4 | #104 | semidirect |
| 421. D4 | #4010 | semidirect |
| 459. C5 | #8991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#700 | 2 |
| #10612679 | 2 |
| #10604678 | 2 |
| #10604650 | 2 |
| C4×#4007 | 2 |
| #10598594 | 2 |
| #10598588 | 2 |
| #8991 | 5 |