Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
380 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 5. #65473 | C2 | semidirect |
| 6. #65471 | C2 | semidirect |
| 8. #65080 | C2 | semidirect |
| 9. #65078 | C2 | semidirect |
| 234. C5 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic5 | 2 |
| #65956 | 2 |
| C5×#451 | 2 |
| #65517 | 2 |
| #65473 | 2 |
| #65471 | 2 |
| #65332 | 2 |
| #65080 | 2 |
| #65078 | 2 |
| #65010 | 2 |
| #65008 | 2 |
| #3113 | 5 |