Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
774 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10615820 | C2 | semidirect |
| 3. C5×#1789 | C2 | semidirect |
| 4. #10600770 | C2 | semidirect |
| 5. #10600249 | C2 | semidirect |
| 6. #10598176 | C2 | semidirect |
| 7. #10598109 | C2 | semidirect |
| 9. C2×#4095 | C4 | semidirect |
| 16. #65521 | C4 | semidirect |
| 79. #1789 | D5 | semidirect |
| 184. C5×Q8 | #99 | semidirect |
| 392. Q8 | #3938 | semidirect |
| 433. C5 | #9368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615820 | 2 |
| #10615813 | 2 |
| C5×#1789 | 2 |
| #10600770 | 2 |
| #10600249 | 2 |
| #10598176 | 2 |
| #10598109 | 2 |
| #9368 | 5 |