Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
510 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 510 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 |
|---|---|---|
| 1. C2×#4086 | C2 | semidirect |
| 2. C22×#686 | C2 | semidirect |
| 3. C22×D40 | C2 | semidirect |
| 4. C2×C5×#102 | C2 | semidirect |
| 5. #65277 | C2 | semidirect |
| 6. C2×#3941 | C2 | semidirect |
| 7. #64770 | C2 | semidirect |
| 54. C2×D20 | D4 | semidirect |
| 57. C2×C5×C8 | D4 | semidirect |
| 66. C2×#168 | D4 | semidirect |
| 72. C2×#102 | D5 | semidirect |
| 106. C2×Dic5 | D8 | semidirect |
| 196. C2×C8 | C22⋊D5 | semidirect |
| 252. C5 | #2011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4086 | 2 |
| C22×#686 | 2 |
| C22×D40 | 2 |
| C2×C5×#102 | 2 |
| #65277 | 2 |
| C2×#3941 | 2 |
| #64770 | 2 |
| #2011 | 5 |