Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 86 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×#3998 | C2 | semidirect |
| 3. #64912 | C2 | semidirect |
| 107. C5 | #2115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4094 | 2 |
| C2×#3998 | 2 |
| #64912 | 2 |
| #2115 | 5 |