Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. C5×#462 | C2 | semidirect |
| 5. #65471 | C2 | semidirect |
| 6. #65379 | C2 | semidirect |
| 7. #65310 | C2 | semidirect |
| 8. #65139 | C2 | semidirect |
| 11. #65083 | C2 | semidirect |
| 91. #462 | D5 | semidirect |
| 113. C4×D5 | Q16 | semidirect |
| 237. C5 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| #65912 | 2 |
| C5×#462 | 2 |
| #65477 | 2 |
| #65471 | 2 |
| #65379 | 2 |
| #65310 | 2 |
| #65139 | 2 |
| D5×C4⋊C8 | 2 |
| #65102 | 2 |
| #65083 | 2 |
| #3249 | 5 |