Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 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 |
|---|---|---|
| 1. #66100 | C2 | semidirect |
| 2. C2×C5×Q32 | C2 | semidirect |
| 3. #65468 | C2 | semidirect |
| 4. #65208 | C2 | semidirect |
| 5. #65207 | C2 | semidirect |
| 6. D5×Q32 | C2 | semidirect |
| 7. #65193 | C2 | semidirect |
| 8. #65190 | C2 | semidirect |
| 57. C2×Q32 | D5 | semidirect |
| 150. C5 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66100 | 2 |
| C2×C5×Q32 | 2 |
| #65468 | 2 |
| #65208 | 2 |
| #65207 | 2 |
| D5×Q32 | 2 |
| #65193 | 2 |
| #65190 | 2 |
| #3417 | 5 |