Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 2. C5×#405 | C2 | semidirect |
| 3. #65428 | C2 | semidirect |
| 4. #65395 | C2 | semidirect |
| 5. #65295 | C2 | semidirect |
| 11. C2×Dic20 | C4 | semidirect |
| 16. C2×D40 | C4 | semidirect |
| 17. C2×#677 | C4 | semidirect |
| 59. #405 | D5 | semidirect |
| 174. C5 | #1976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4050 | 2 |
| C5×#405 | 2 |
| #65428 | 2 |
| #65395 | 2 |
| #65295 | 2 |
| #1976 | 5 |