Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. Q8×D20 | C2 | semidirect |
| 2. #65316 | C2 | semidirect |
| 4. #64983 | C2 | semidirect |
| 5. C5×Q8⋊C8 | C2 | semidirect |
| 6. #64706 | C2 | semidirect |
| 7. #64679 | C2 | semidirect |
| 57. Q8⋊C8 | D5 | semidirect |
| 62. C5×Q8 | D8 | semidirect |
| 76. D20 | SD16 | semidirect |
| 156. Q8 | D40 | semidirect |
| 177. C5 | #1627 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D20 | 2 |
| #65316 | 2 |
| #65132 | 2 |
| #64983 | 2 |
| C5×Q8⋊C8 | 2 |
| #64706 | 2 |
| #64679 | 2 |
| #1627 | 5 |