Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. C5×#1971 | C2 | semidirect |
| 4. #10602854 | C2 | semidirect |
| 6. #10598212 | C2 | semidirect |
| 7. #10598155 | C2 | semidirect |
| 17. #65468 | C4 | semidirect |
| 36. C2×C5×Q16 | C2×C4 | semidirect |
| 69. #3944 | C2×C4 | semidirect |
| 76. #1971 | D5 | semidirect |
| 196. C2×Q16 | C4×D5 | semidirect |
| 332. C5 | #13026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65468 | 2 |
| #10610225 | 2 |
| C5×#1971 | 2 |
| #10602854 | 2 |
| C2×#64708 | 2 |
| #10598212 | 2 |
| #10598155 | 2 |
| #13026 | 5 |