Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#4004 | C2 | semidirect |
| 3. C2×#4003 | C2 | semidirect |
| 4. C2×#4002 | C2 | semidirect |
| 33. C2×#170 | D4 | semidirect |
| 138. C5 | #1955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4039 | 2 |
| C2×#4004 | 2 |
| C2×#4003 | 2 |
| C2×#4002 | 2 |
| #1955 | 5 |