Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 6. C5×#500 | C4 | semidirect |
| 7. C5×#494 | C4 | semidirect |
| 12. C4×C5×Q16 | C4 | semidirect |
| 80. #500 | Dic5 | semidirect |
| 81. #494 | Dic5 | semidirect |
| 86. C4×Q16 | Dic5 | semidirect |
| 212. C5 | #11859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3170 | 2 |
| #10600556 | 2 |
| #10600538 | 2 |
| #10598267 | 2 |
| #11859 | 5 |