Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 192 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×C5×#681 | C2 | semidirect |
| 3. #11716936 | C2 | semidirect |
| 4. #11716935 | C2 | semidirect |
| 13. C5×#681 | C22 | semidirect |
| 14. C2×C5×#168 | C22 | semidirect |
| 15. #87769 | C22 | semidirect |
| 16. #87767 | C22 | semidirect |
| 34. C2×#681 | D5 | semidirect |
| 67. #681 | C2×D5 | semidirect |
| 68. C2×#168 | C2×D5 | semidirect |
| 111. C52 | #568 | semidirect |
| 167. C5 | #66079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C5×#681 | 2 |
| #11716936 | 2 |
| #11716935 | 2 |
| #66079 | 5 |