Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
690 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. #10604669 | C2 | semidirect |
| 4. #10604667 | C2 | semidirect |
| 6. #10598530 | C2 | semidirect |
| 7. #10598530 | C2 | semidirect |
| 21. C5×#486 | C4 | semidirect |
| 22. #65377 | C4 | semidirect |
| 23. #65359 | C4 | semidirect |
| 26. #64983 | C4 | semidirect |
| 52. C5×C4⋊Q8 | C2×C4 | semidirect |
| 65. #4015 | C2×C4 | semidirect |
| 75. C4×C5×C8 | C2×C4 | semidirect |
| 80. C4×#168 | C2×C4 | semidirect |
| 169. #486 | AGL(1,𝔽5) | semidirect |
| 263. C4⋊Q8 | C2×AGL(1,𝔽5) | semidirect |
| 297. C4×C8 | C2×AGL(1,𝔽5) | semidirect |
| 482. C5 | #9057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617369 | 2 |
| D5×#486 | 2 |
| #10604669 | 2 |
| #10604667 | 2 |
| D5⋊#331 | 2 |
| #10598530 | 2 |
| #9057 | 5 |