Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
298 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 1. C2×C5×#677 | C2 | semidirect |
| 2. Dic5×D20 | C2 | semidirect |
| 3. #11716982 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 6. C5×#3946 | C2 | semidirect |
| 7. #11716607 | C2 | semidirect |
| 44. C2×#677 | D5 | semidirect |
| 53. #3946 | D5 | semidirect |
| 147. C52 | #463 | semidirect |
| 225. C5 | #65133 | semidirect |
| 226. C5 | #65454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#677 | 2 |
| Dic5×D20 | 2 |
| #11716982 | 2 |
| C2×#87771 | 2 |
| #11716688 | 2 |
| C5×#3946 | 2 |
| #11716607 | 2 |
| #65454 | 5 |
| #65133 | 5 |