Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #10602385 | C2 | semidirect |
| 3. #10602365 | C2 | semidirect |
| 4. #10598142 | C2 | semidirect |
| 6. C2×C4×C5×D4 | C4 | semidirect |
| 9. C5×#400 | C4 | semidirect |
| 11. C5×#394 | C4 | semidirect |
| 17. C5×#383 | C4 | semidirect |
| 111. C2×C4×D4 | Dic5 | semidirect |
| 115. #400 | Dic5 | semidirect |
| 117. #394 | Dic5 | semidirect |
| 123. #383 | Dic5 | semidirect |
| 350. C5 | #11754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2598 | 2 |
| #10602385 | 2 |
| #10602365 | 2 |
| #10598142 | 2 |
| #10598136 | 2 |
| #11754 | 5 |