Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#65149 | C2 | semidirect |
| 3. C2×#64738 | C2 | semidirect |
| 4. #10602224 | C2 | semidirect |
| 5. C2×#64708 | C2 | semidirect |
| 6. C5×#1386 | C2 | semidirect |
| 7. #10598217 | C2 | semidirect |
| 19. #65176 | C4 | semidirect |
| 20. #65172 | C4 | semidirect |
| 63. C5×#106 | D4 | semidirect |
| 65. #3949 | D4 | semidirect |
| 78. #1386 | D5 | semidirect |
| 231. #106 | D20 | semidirect |
| 352. C5 | #13002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610911 | 2 |
| C2×#65149 | 2 |
| C2×#64738 | 2 |
| #10602224 | 2 |
| C2×#64708 | 2 |
| C5×#1386 | 2 |
| #10598217 | 2 |
| #13002 | 5 |