Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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×#462 | C2 | semidirect |
| 5. #65470 | C2 | semidirect |
| 6. #65379 | C2 | semidirect |
| 7. #65320 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 11. #65081 | C2 | semidirect |
| 92. #462 | D5 | semidirect |
| 117. C4×D5 | Q16 | semidirect |
| 249. C5 | #3209 | 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×#462 | 2 |
| #65475 | 2 |
| #65470 | 2 |
| #65379 | 2 |
| #65320 | 2 |
| #65138 | 2 |
| #65122 | 2 |
| #65097 | 2 |
| #65081 | 2 |
| #3209 | 5 |