Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
936 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 245 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. C4×C52×D4 | C2 | semidirect |
| 3. #11717256 | C2 | semidirect |
| 4. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 5. #11717246 | C2 | semidirect |
| 6. #11717217 | C2 | semidirect |
| 7. #11717210 | C2 | semidirect |
| 8. #11717203 | C2 | semidirect |
| 9. #11717199 | C2 | semidirect |
| 10. C42×C5⋊D5 | C2 | semidirect |
| 11. C4×#6045 | C2 | semidirect |
| 54. C4×C5×D4 | D5 | semidirect |
| 136. C4×D4 | C5⋊D5 | semidirect |
| 139. C52 | #529 | semidirect |
| 202. C5 | #65891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C52×D4 | 2 |
| #11717258 | 2 |
| #11717256 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717246 | 2 |
| #11717217 | 2 |
| #11717210 | 2 |
| #11717203 | 2 |
| #11717199 | 2 |
| C42×C5⋊D5 | 2 |
| C4×#6045 | 2 |
| #65891 | 5 |