Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
586 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 124 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. C2×#64913 | C2 | semidirect |
| 5. #10598706 | C2 | semidirect |
| 35. C5×#123 | C8 | semidirect |
| 82. C22×C4×C5 | C2×C8 | semidirect |
| 105. C5×C22⋊C4 | C2×C8 | semidirect |
| 193. #123 | #170 | semidirect |
| 275. C22×C4 | C2×#170 | semidirect |
| 294. C22⋊C4 | C2×#170 | semidirect |
| 353. C5 | #9108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617497 | 2 |
| #10614567 | 2 |
| #10604931 | 2 |
| C2×#64913 | 2 |
| #10598706 | 2 |
| #9108 | 5 |