Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
774 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2341 | C2 | semidirect |
| 3. #10602931 | C2 | semidirect |
| 4. #10600321 | C2 | semidirect |
| 5. #10600237 | C2 | semidirect |
| 6. #10598117 | C2 | semidirect |
| 7. #10598109 | C2 | semidirect |
| 10. C2×#4095 | C4 | semidirect |
| 20. #65521 | C4 | semidirect |
| 77. #2341 | 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 |
|---|---|
| C5×#2341 | 2 |
| #10615813 | 2 |
| #10602931 | 2 |
| #10600321 | 2 |
| #10600237 | 2 |
| #10598117 | 2 |
| #10598109 | 2 |
| #9368 | 5 |