Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
398 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. #65788 | C2 | semidirect |
| 3. #65704 | C2 | semidirect |
| 4. #65702 | C2 | semidirect |
| 5. #65683 | C2 | semidirect |
| 6. #65681 | C2 | semidirect |
| 7. #65680 | C2 | semidirect |
| 8. D5⋊(C4⋊C8) | C2 | semidirect |
| 82. D20 | M16 | semidirect |
| 192. C5 | #2990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#713 | 2 |
| #65788 | 2 |
| #65704 | 2 |
| #65702 | 2 |
| #65683 | 2 |
| #65681 | 2 |
| #65680 | 2 |
| D5⋊(C4⋊C8) | 2 |
| #2990 | 5 |