Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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. #66064 | C2 | semidirect |
| 2. #66061 | C2 | semidirect |
| 3. C5×#498 | C2 | semidirect |
| 4. #65376 | C2 | semidirect |
| 5. #65373 | C2 | semidirect |
| 6. #65160 | C2 | semidirect |
| 7. #65159 | C2 | semidirect |
| 9. #65145 | C2 | semidirect |
| 11. #64968 | C2 | semidirect |
| 73. D40 | Q8 | semidirect |
| 77. #498 | D5 | semidirect |
| 101. D20 | C2×Q8 | semidirect |
| 109. 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 |
|---|---|
| #66064 | 2 |
| #66061 | 2 |
| C5×#498 | 2 |
| #65376 | 2 |
| #65373 | 2 |
| #65160 | 2 |
| #65159 | 2 |
| #65158 | 2 |
| #65145 | 2 |
| C4×D40 | 2 |
| #64968 | 2 |
| #3384 | 5 |