Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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×#501 | C2 | semidirect |
| 4. #65369 | C2 | semidirect |
| 5. #65354 | C2 | semidirect |
| 7. #65167 | C2 | semidirect |
| 9. #65147 | C2 | semidirect |
| 11. #64991 | C2 | semidirect |
| 79. #676 | Q8 | semidirect |
| 85. #501 | D5 | semidirect |
| 222. C5 | #3166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| D5×#125 | 2 |
| C5×#501 | 2 |
| #65369 | 2 |
| #65354 | 2 |
| #65170 | 2 |
| #65167 | 2 |
| #65150 | 2 |
| #65147 | 2 |
| #64996 | 2 |
| #64991 | 2 |
| #3166 | 5 |