Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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. C5×#504 | C2 | semidirect |
| 2. #65432 | C2 | semidirect |
| 4. C2×#3932 | C2 | semidirect |
| 5. #64737 | C2 | semidirect |
| 6. #64736 | C2 | semidirect |
| 7. #64726 | C2 | semidirect |
| 45. #504 | D5 | semidirect |
| 130. C5 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#504 | 2 |
| #65432 | 2 |
| #65431 | 2 |
| C2×#3932 | 2 |
| #64737 | 2 |
| #64736 | 2 |
| #64726 | 2 |
| #2223 | 5 |