Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#3996 | C2 | semidirect |
| 4. #64896 | C2 | semidirect |
| 82. C22×C5 | #108 | semidirect |
| 89. C2×D5 | #108 | semidirect |
| 148. C5 | #1810 | semidirect |
| 158. C22 | #3996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D5 | 2 |
| #65756 | 2 |
| C2×#3996 | 2 |
| #64896 | 2 |
| #1810 | 5 |