Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
586 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 126 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. #10604967 | C2 | semidirect |
| 5. #10598696 | C2 | semidirect |
| 27. C5×#124 | C8 | semidirect |
| 62. C2×C5×Q8 | C2×C8 | semidirect |
| 83. C42×C5 | C2×C8 | semidirect |
| 152. #124 | #170 | semidirect |
| 202. C2×Q8 | C2×#170 | semidirect |
| 235. C42 | C2×#170 | semidirect |
| 278. C5 | #8957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617497 | 2 |
| Dic5×#124 | 2 |
| #10604967 | 2 |
| #10604932 | 2 |
| #10598696 | 2 |
| #8957 | 5 |