Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
251 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 84 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. C4×#6032 | C2 | semidirect |
| 3. C4×C5×#170 | C2 | semidirect |
| 4. #11716760 | C2 | semidirect |
| 26. D5×Dic5 | C8 | semidirect |
| 34. C4×#170 | D5 | semidirect |
| 105. C52 | #431 | semidirect |
| 163. C5 | #64974 | semidirect |
| 164. C5 | #65754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×Dic5 | 2 |
| C4×#6032 | 2 |
| C4×C5×#170 | 2 |
| #11716760 | 2 |
| #11716753 | 2 |
| #65754 | 5 |
| #64974 | 5 |