Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 22. #3948 | C4 | semidirect |
| 90. Dic10 | C4⋊C4 | semidirect |
| 194. C5 | #1863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4033 | 2 |
| C2×C5×#107 | 2 |
| C2×#3948 | 2 |
| #65262 | 2 |
| C2×#3942 | 2 |
| #64770 | 2 |
| #64749 | 2 |
| #1863 | 5 |