Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. C5×Q8×C16 | C2 | semidirect |
| 2. #10601735 | C2 | semidirect |
| 5. #10598052 | C2 | semidirect |
| 7. #10597992 | C2 | semidirect |
| 47. Q8×C16 | D5 | semidirect |
| 78. C5×C16 | SD16 | semidirect |
| 96. C5×Q8 | SD32 | semidirect |
| 175. C16 | #688 | semidirect |
| 184. Q8 | #3932 | semidirect |
| 202. C5 | #12441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C16 | 2 |
| #10601735 | 2 |
| #10601732 | 2 |
| #10599854 | 2 |
| #10598052 | 2 |
| #10598051 | 2 |
| #10597992 | 2 |
| #12441 | 5 |