Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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×D40 | C2 | semidirect |
| 2. #10601732 | C2 | semidirect |
| 4. #10599851 | C2 | semidirect |
| 5. C5×Q8⋊C16 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10597995 | C2 | semidirect |
| 59. Q8⋊C16 | D5 | semidirect |
| 91. D40 | SD16 | semidirect |
| 114. C5×Q8 | D16 | semidirect |
| 228. Q8 | D80 | semidirect |
| 251. C5 | #12352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D40 | 2 |
| #10601732 | 2 |
| #10600079 | 2 |
| #10599851 | 2 |
| C5×Q8⋊C16 | 2 |
| #10598055 | 2 |
| #10597995 | 2 |
| #12352 | 5 |