Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C5×Q8 | C2 | semidirect |
| 3. #65520 | C2 | semidirect |
| 4. #65282 | C2 | semidirect |
| 6. #65275 | C2 | semidirect |
| 7. C4×#685 | C2 | semidirect |
| 8. #65221 | C2 | semidirect |
| 51. C2×C4×Q8 | D5 | semidirect |
| 171. C5 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×Q8 | 2 |
| C2×C4×D20 | 2 |
| #65520 | 2 |
| #65282 | 2 |
| #65280 | 2 |
| #65275 | 2 |
| C4×#685 | 2 |
| #65221 | 2 |
| #2398 | 5 |