Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 500 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. Q8×#700 | C2 | semidirect |
| 5. C4×#4009 | C2 | semidirect |
| 6. #10598594 | C2 | semidirect |
| 7. #10598588 | C2 | semidirect |
| 22. C5×#475 | C4 | semidirect |
| 23. #65383 | C4 | semidirect |
| 24. #65316 | C4 | semidirect |
| 27. #65137 | C4 | semidirect |
| 126. #700 | SD16 | semidirect |
| 156. #475 | AGL(1,𝔽5) | semidirect |
| 185. C5×Q8 | #104 | semidirect |
| 372. Q8 | #4010 | semidirect |
| 411. C5 | #8992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#700 | 2 |
| #10612727 | 2 |
| #10604678 | 2 |
| #10604650 | 2 |
| C4×#4009 | 2 |
| #10598594 | 2 |
| #10598588 | 2 |
| #8992 | 5 |