Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
277 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #11716845 | C2 | semidirect |
| 5. C4×C5×#170 | C2 | semidirect |
| 6. #11716752 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 13. #87829 | C4 | semidirect |
| 14. #87827 | C4 | semidirect |
| 45. C4×#170 | D5 | semidirect |
| 129. C52 | #405 | semidirect |
| 197. C5 | #64978 | semidirect |
| 198. C5 | #65701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| C2×#87827 | 2 |
| #11716954 | 2 |
| #11716845 | 2 |
| C4×C5×#170 | 2 |
| #11716752 | 2 |
| Dic5×#170 | 2 |
| #65701 | 5 |
| #64978 | 5 |