Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11716975 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. C2×#87768 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 6. C5×#3939 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 53. #3939 | D5 | semidirect |
| 139. #168 | D20 | semidirect |
| 147. C52 | #468 | semidirect |
| 222. C5 | #65175 | semidirect |
| 223. C5 | #65331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4041 | 2 |
| #11716975 | 2 |
| C2×#87773 | 2 |
| C2×#87768 | 2 |
| #11716677 | 2 |
| C5×#3939 | 2 |
| #11716603 | 2 |
| #65331 | 5 |
| #65175 | 5 |