Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
252 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 252 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. #11717036 | C2 | semidirect |
| 3. #11716675 | C2 | semidirect |
| 4. C5×#3940 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 29. C5×D20 | Q8 | semidirect |
| 47. #3940 | D5 | semidirect |
| 111. D20 | Dic10 | semidirect |
| 127. C52 | #476 | semidirect |
| 191. C5 | #65159 | semidirect |
| 192. C5 | #65297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| #11717036 | 2 |
| #11716675 | 2 |
| C5×#3940 | 2 |
| #11716612 | 2 |
| #11716604 | 2 |
| #11716603 | 2 |
| #65297 | 5 |
| #65159 | 5 |