Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 125 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. #65877 | C2 | semidirect |
| 3. C5×#436 | C2 | semidirect |
| 4. #65423 | C2 | semidirect |
| 5. #65410 | C2 | semidirect |
| 6. #65139 | C2 | semidirect |
| 7. #65131 | C2 | semidirect |
| 8. #65025 | C2 | semidirect |
| 9. #65012 | C2 | semidirect |
| 10. C4×#677 | C2 | semidirect |
| 11. #64971 | C2 | semidirect |
| 83. #436 | D5 | semidirect |
| 220. C5 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65897 | 2 |
| #65877 | 2 |
| C5×#436 | 2 |
| #65423 | 2 |
| #65410 | 2 |
| #65139 | 2 |
| #65131 | 2 |
| #65025 | 2 |
| #65012 | 2 |
| C4×#677 | 2 |
| #64971 | 2 |
| #3357 | 5 |