Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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×#493 | C2 | semidirect |
| 2. #65436 | C2 | semidirect |
| 3. #64989 | C2 | semidirect |
| 4. #64783 | C2 | semidirect |
| 5. #64683 | C2 | semidirect |
| 29. Dic20 | D4 | semidirect |
| 30. D40 | D4 | semidirect |
| 36. #493 | D5 | semidirect |
| 110. C5 | #2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#493 | 2 |
| #65436 | 2 |
| #64989 | 2 |
| #64783 | 2 |
| #64683 | 2 |
| #2213 | 5 |