Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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×#477 | C2 | semidirect |
| 4. #65380 | C2 | semidirect |
| 5. #65310 | C2 | semidirect |
| 7. #65163 | C2 | semidirect |
| 8. #65139 | C2 | semidirect |
| 11. #65081 | C2 | semidirect |
| 89. #477 | D5 | semidirect |
| 235. C5 | #3230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C4⋊Q8 | 2 |
| #65912 | 2 |
| C5×#477 | 2 |
| #65380 | 2 |
| #65310 | 2 |
| #65173 | 2 |
| #65163 | 2 |
| #65139 | 2 |
| #65122 | 2 |
| #65098 | 2 |
| #65081 | 2 |
| #3230 | 5 |