Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 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. C2×#4093 | C2 | semidirect |
| 2. C22×#688 | C2 | semidirect |
| 4. C2×C5×#103 | C2 | semidirect |
| 5. #65277 | C2 | semidirect |
| 6. C2×#3941 | C2 | semidirect |
| 7. #64770 | C2 | semidirect |
| 69. C2×#103 | D5 | semidirect |
| 237. C5 | #2012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4093 | 2 |
| C22×#688 | 2 |
| C22×D40 | 2 |
| C2×C5×#103 | 2 |
| #65277 | 2 |
| C2×#3941 | 2 |
| #64770 | 2 |
| #2012 | 5 |