Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22×#689 | C2 | semidirect |
| 4. C5×#391 | C2 | semidirect |
| 5. C2×#3942 | C2 | semidirect |
| 7. #64744 | C2 | semidirect |
| 70. #391 | D5 | semidirect |
| 226. C5 | #2015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#689 | 2 |
| C22×#688 | 2 |
| C2×#4021 | 2 |
| C5×#391 | 2 |
| C2×#3942 | 2 |
| C2×#3941 | 2 |
| #64744 | 2 |
| #2015 | 5 |