Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. #65904 | C2 | semidirect |
| 3. C5×C8×Q8 | C2 | semidirect |
| 4. #65137 | C2 | semidirect |
| 5. #65130 | C2 | semidirect |
| 6. #64982 | C2 | semidirect |
| 7. C4×#677 | C2 | semidirect |
| 50. C8×Q8 | D5 | semidirect |
| 53. C5×Q8 | SD16 | semidirect |
| 68. C5×C8 | #41 | semidirect |
| 123. Q8 | #677 | semidirect |
| 136. C8 | #713 | semidirect |
| 137. C5 | #3392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65911 | 2 |
| #65904 | 2 |
| C5×C8×Q8 | 2 |
| #65137 | 2 |
| #65130 | 2 |
| #64982 | 2 |
| C4×#677 | 2 |
| #3392 | 5 |