Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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×#4064 | C2 | semidirect |
| 3. C2×D5×Q16 | C2 | semidirect |
| 4. #66058 | C2 | semidirect |
| 5. C5×#494 | C2 | semidirect |
| 6. #65480 | C2 | semidirect |
| 7. #65479 | C2 | semidirect |
| 8. #65470 | C2 | semidirect |
| 9. #65375 | C2 | semidirect |
| 10. #64985 | C2 | semidirect |
| 11. #64978 | C2 | semidirect |
| 87. #494 | D5 | semidirect |
| 225. C5 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4065 | 2 |
| C2×#4064 | 2 |
| C2×D5×Q16 | 2 |
| #66058 | 2 |
| C5×#494 | 2 |
| #65480 | 2 |
| #65479 | 2 |
| #65470 | 2 |
| #65375 | 2 |
| #64985 | 2 |
| #64978 | 2 |
| #3156 | 5 |