Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #65913 | C2 | semidirect |
| 2. Q8×D20 | C2 | semidirect |
| 3. C5×#446 | C2 | semidirect |
| 4. #65136 | C2 | semidirect |
| 5. #65135 | C2 | semidirect |
| 6. #65131 | C2 | semidirect |
| 7. #65131 | C2 | semidirect |
| 9. #64991 | C2 | semidirect |
| 11. #64969 | C2 | semidirect |
| 73. D40 | Q8 | semidirect |
| 82. #446 | D5 | semidirect |
| 100. D20 | C2×Q8 | semidirect |
| 110. C5×C8 | C2×Q8 | semidirect |
| 219. C8 | Q8×D5 | semidirect |
| 220. C5 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65913 | 2 |
| Q8×D20 | 2 |
| C5×#446 | 2 |
| #65136 | 2 |
| #65135 | 2 |
| #65131 | 2 |
| #65000 | 2 |
| #64991 | 2 |
| C4×D40 | 2 |
| #64969 | 2 |
| #3384 | 5 |