Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
235 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11716845 | C2 | semidirect |
| 3. C5×#4002 | C2 | semidirect |
| 4. #11716760 | C2 | semidirect |
| 34. #4002 | D5 | semidirect |
| 105. C52 | #432 | semidirect |
| 163. C5 | #64994 | semidirect |
| 164. C5 | #65757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×Dic5 | 2 |
| #11716845 | 2 |
| C5×#4002 | 2 |
| #11716760 | 2 |
| #11716753 | 2 |
| #65757 | 5 |
| #64994 | 5 |