Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. D5×C4⋊Q8 | C2 | semidirect |
| 3. C5×#461 | C2 | semidirect |
| 5. #65456 | C2 | semidirect |
| 6. #65379 | C2 | semidirect |
| 7. #65308 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 9. #65124 | C2 | semidirect |
| 10. #65097 | C2 | semidirect |
| 11. #65086 | C2 | semidirect |
| 92. #461 | D5 | semidirect |
| 254. C5 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| #65891 | 2 |
| C5×#461 | 2 |
| #65459 | 2 |
| #65456 | 2 |
| #65379 | 2 |
| #65308 | 2 |
| #65138 | 2 |
| #65124 | 2 |
| #65097 | 2 |
| #65086 | 2 |
| #3218 | 5 |