Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
394 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 168 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. Q8×#170 | C2 | semidirect |
| 3. #65705 | C2 | semidirect |
| 4. #65681 | C2 | semidirect |
| 5. #65680 | C2 | semidirect |
| 42. C5×Q8 | M16 | semidirect |
| 101. Q8 | #700 | semidirect |
| 115. C5 | #2991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#713 | 2 |
| Q8×#170 | 2 |
| #65705 | 2 |
| #65681 | 2 |
| #65680 | 2 |
| #2991 | 5 |