Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 4. #10601542 | C2 | semidirect |
| 5. #10601234 | C2 | semidirect |
| 6. #10598227 | C2 | semidirect |
| 7. #10598198 | C2 | semidirect |
| 18. C5×#332 | C4 | semidirect |
| 19. C5×#331 | C4 | semidirect |
| 114. #332 | Dic5 | semidirect |
| 115. #331 | Dic5 | semidirect |
| 285. C5 | #9582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1540 | 2 |
| #10602608 | 2 |
| #10602593 | 2 |
| #10601542 | 2 |
| #10601234 | 2 |
| #10598227 | 2 |
| #10598198 | 2 |
| #9582 | 5 |