Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
602 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C5×#3103 | C2 | semidirect |
| 3. #10614232 | C2 | semidirect |
| 4. #10602607 | C2 | semidirect |
| 5. #10602415 | C2 | semidirect |
| 6. #10601550 | C2 | semidirect |
| 7. #10598229 | C2 | semidirect |
| 85. #3103 | D5 | semidirect |
| 118. C2×D20 | SD16 | semidirect |
| 431. C5 | #9998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3103 | 2 |
| #10615028 | 2 |
| #10614232 | 2 |
| #10602607 | 2 |
| #10602415 | 2 |
| #10601550 | 2 |
| #10598229 | 2 |
| #9998 | 5 |