Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
209 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 62 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. #11716760 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 6. #11716752 | C2 | semidirect |
| 7. Dic5×#170 | C2 | semidirect |
| 123. C52 | #433 | semidirect |
| 189. C5 | #65009 | semidirect |
| 190. C5 | #65697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717073 | 2 |
| C22⋊#6032 | 2 |
| C5×C22⋊#170 | 2 |
| #11716760 | 2 |
| #11716759 | 2 |
| #11716752 | 2 |
| Dic5×#170 | 2 |
| #65697 | 5 |
| #65009 | 5 |