Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
314 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 1. #11717217 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 4. C2×#87769 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. C5×#3939 | C2 | semidirect |
| 7. #11716608 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 52. #3941 | D5 | semidirect |
| 53. #3939 | D5 | semidirect |
| 144. #168 | D20 | semidirect |
| 152. C52 | #468 | semidirect |
| 232. C5 | #65069 | semidirect |
| 233. C5 | #65175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717217 | 2 |
| #11717034 | 2 |
| C2×#87773 | 2 |
| C2×#87769 | 2 |
| C5×#3941 | 2 |
| C5×#3939 | 2 |
| #11716608 | 2 |
| #65175 | 5 |
| #65069 | 5 |