Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×#4133 | C2 | semidirect |
| 2. C2×#4131 | C2 | semidirect |
| 4. #65787 | C2 | semidirect |
| 5. #65776 | C2 | semidirect |
| 6. #65695 | C2 | semidirect |
| 7. #65692 | C2 | semidirect |
| 8. #65682 | C2 | semidirect |
| 9. C4×D5⋊C8 | C2 | semidirect |
| 62. D5⋊C8 | D4 | semidirect |
| 141. Dic5 | #131 | semidirect |
| 211. C5 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4133 | 2 |
| C2×#4131 | 2 |
| #66002 | 2 |
| #65787 | 2 |
| #65776 | 2 |
| #65695 | 2 |
| #65692 | 2 |
| #65682 | 2 |
| C4×D5⋊C8 | 2 |
| #2931 | 5 |