Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 101 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×#2535 | C2 | semidirect |
| 2. #10614039 | C2 | semidirect |
| 3. #10614038 | C2 | semidirect |
| 4. #10602391 | C2 | semidirect |
| 5. #10602390 | C2 | semidirect |
| 6. #10600338 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 67. #4020 | D4 | semidirect |
| 70. #4015 | D4 | semidirect |
| 84. C4⋊#168 | D4 | semidirect |
| 86. C4×#168 | D4 | semidirect |
| 89. #2535 | D5 | semidirect |
| 107. C2×C5×D4 | D8 | semidirect |
| 356. C2×D4 | #686 | semidirect |
| 472. C5 | #9996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2535 | 2 |
| #10614039 | 2 |
| #10614038 | 2 |
| #10602391 | 2 |
| #10602390 | 2 |
| #10600338 | 2 |
| #10598122 | 2 |
| #9996 | 5 |