Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #65901 | C2 | semidirect |
| 3. C5×#446 | C2 | semidirect |
| 4. #65140 | C2 | semidirect |
| 5. #65139 | C2 | semidirect |
| 9. #64991 | C2 | semidirect |
| 11. #64971 | C2 | semidirect |
| 73. #677 | Q8 | semidirect |
| 82. #446 | D5 | semidirect |
| 105. Dic10 | C2×Q8 | semidirect |
| 108. C5×C8 | C2×Q8 | semidirect |
| 212. C8 | Q8×D5 | semidirect |
| 213. C5 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D20 | 2 |
| #65901 | 2 |
| C5×#446 | 2 |
| #65140 | 2 |
| #65139 | 2 |
| #65136 | 2 |
| #65135 | 2 |
| #64999 | 2 |
| #64991 | 2 |
| C4×#677 | 2 |
| #64971 | 2 |
| #3386 | 5 |