Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
770 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 128 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. #10598704 | C2 | direct (N × H) |
| 35. C2×C5×C22⋊C4 | C8 | semidirect |
| 98. C5×C22⋊C4 | C2×C8 | semidirect |
| 198. C2×C22⋊C4 | #170 | semidirect |
| 289. C22⋊C4 | C2×#170 | semidirect |
| 296. C2×C5 | #1326 | semidirect |
| 355. C5 | C2×#1326 | semidirect |
| 397. C2 | #10598704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65239 | 2 |
| C2×#64933 | 2 |
| #10598704 | 2 |
| C2×#1326 | 5 |