Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C5×#413 | C2 | semidirect |
| 3. #65525 | C2 | semidirect |
| 4. #65420 | C2 | semidirect |
| 5. C2×#3955 | C2 | semidirect |
| 6. #65413 | C2 | semidirect |
| 7. #64776 | C2 | semidirect |
| 63. #413 | D5 | semidirect |
| 198. C5 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4095 | 2 |
| C5×#413 | 2 |
| #65525 | 2 |
| #65420 | 2 |
| C2×#3955 | 2 |
| #65413 | 2 |
| #64776 | 2 |
| #2048 | 5 |