Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
434 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 121 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×#532 | C2 | semidirect |
| 2. #65811 | C2 | semidirect |
| 3. #65378 | C2 | semidirect |
| 4. #65363 | C2 | semidirect |
| 5. #65326 | C2 | semidirect |
| 6. #65308 | C2 | semidirect |
| 7. #65304 | C2 | semidirect |
| 8. #65215 | C2 | semidirect |
| 67. #532 | D5 | semidirect |
| 210. C5 | #3214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#532 | 2 |
| #65811 | 2 |
| #65378 | 2 |
| #65363 | 2 |
| #65326 | 2 |
| #65308 | 2 |
| #65304 | 2 |
| #65215 | 2 |
| #3214 | 5 |