Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#4036 | C2 | semidirect |
| 5. #65259 | C2 | semidirect |
| 6. #65147 | C2 | semidirect |
| 7. #65146 | C2 | semidirect |
| 8. #65057 | C2 | semidirect |
| 9. #65052 | C2 | semidirect |
| 10. #65010 | C2 | semidirect |
| 11. #65007 | C2 | semidirect |
| 227. C5 | #3232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65934 | 2 |
| C2×#4036 | 2 |
| C5×#481 | 2 |
| #65322 | 2 |
| #65259 | 2 |
| #65147 | 2 |
| #65146 | 2 |
| #65057 | 2 |
| #65052 | 2 |
| #65010 | 2 |
| #65007 | 2 |
| #3232 | 5 |