Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 1. #10613738 | C2 | semidirect |
| 3. #10602243 | C2 | semidirect |
| 4. #10601457 | C2 | semidirect |
| 5. #10601449 | C2 | semidirect |
| 6. C5×#1386 | C2 | semidirect |
| 7. #10598212 | C2 | semidirect |
| 21. #65157 | C4 | semidirect |
| 22. #65154 | C4 | semidirect |
| 54. C5×M32 | D4 | semidirect |
| 63. #3944 | D4 | semidirect |
| 76. #1386 | D5 | semidirect |
| 213. M32 | D20 | semidirect |
| 338. C5 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613738 | 2 |
| #10610851 | 2 |
| #10602243 | 2 |
| #10601457 | 2 |
| #10601449 | 2 |
| C5×#1386 | 2 |
| #10598212 | 2 |
| #13077 | 5 |