Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
273 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 273 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. C4×#6032 | C2 | semidirect |
| 5. C5×#4002 | C2 | semidirect |
| 6. #11716752 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 13. #87828 | C4 | semidirect |
| 14. D5×#170 | C4 | semidirect |
| 43. #4002 | D5 | semidirect |
| 129. C52 | #405 | semidirect |
| 194. C5 | #64997 | semidirect |
| 195. C5 | #65691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87828 | 2 |
| C2×D5×#170 | 2 |
| #11716995 | 2 |
| C4×#6032 | 2 |
| C5×#4002 | 2 |
| #11716752 | 2 |
| Dic5×#170 | 2 |
| #65691 | 5 |
| #64997 | 5 |