Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
592 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 4. #10598142 | C2 | semidirect |
| 5. #10598137 | C2 | semidirect |
| 6. C2×C5×C22⋊Q8 | C4 | semidirect |
| 9. C5×#399 | C4 | semidirect |
| 13. C5×#393 | C4 | semidirect |
| 16. C5×#380 | C4 | semidirect |
| 25. C22×C5×Q8 | C2×C4 | semidirect |
| 35. C2×C5×C4⋊C4 | C2×C4 | semidirect |
| 55. C5×#95 | C2×C4 | semidirect |
| 56. C5×#95 | C2×C4 | semidirect |
| 115. C2×C22⋊Q8 | Dic5 | semidirect |
| 119. #399 | Dic5 | semidirect |
| 123. #393 | Dic5 | semidirect |
| 126. #380 | Dic5 | semidirect |
| 192. C22×Q8 | C2×Dic5 | semidirect |
| 203. C2×C4⋊C4 | C2×Dic5 | semidirect |
| 224. #95 | C2×Dic5 | semidirect |
| 225. #95 | C2×Dic5 | semidirect |
| 384. C5 | #11716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2626 | 2 |
| C2×#64746 | 2 |
| C2×#64745 | 2 |
| #10598142 | 2 |
| #10598137 | 2 |
| #11716 | 5 |