Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11717425 | C2 | semidirect |
| 3. C2×C5×D5⋊C8 | C2 | semidirect |
| 4. #11716737 | C2 | semidirect |
| 5. #11716735 | C2 | semidirect |
| 6. #87900 | C4 | semidirect |
| 7. C5×#709 | C4 | semidirect |
| 13. #87874 | C4 | semidirect |
| 15. #87870 | C4 | semidirect |
| 53. C2×D5⋊C8 | D5 | semidirect |
| 91. #709 | AGL(1,𝔽5) | semidirect |
| 176. C52 | #416 | semidirect |
| 268. C5 | #65402 | semidirect |
| 269. C5 | #65794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#709 | 2 |
| #11717425 | 2 |
| C2×C5×D5⋊C8 | 2 |
| #11716737 | 2 |
| #11716735 | 2 |
| #65794 | 5 |
| #65402 | 5 |