Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 6. C2×C5×C4⋊C4 | C4 | semidirect |
| 8. C2×C42×C5 | C4 | semidirect |
| 41. C2×C4⋊C4 | Dic5 | semidirect |
| 44. C2×C42 | Dic5 | semidirect |
| 84. C5 | #1820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#117 | 2 |
| #65500 | 2 |
| #64746 | 2 |
| #1820 | 5 |