Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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. C5×#4039 | C2 | semidirect |
| 2. Dic5×D20 | C2 | semidirect |
| 4. #11716675 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. #11716604 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 19. #87770 | C4 | semidirect |
| 31. C5×D20 | C2×C4 | semidirect |
| 32. C5×D20 | C2×C4 | semidirect |
| 35. #6029 | C2×C4 | semidirect |
| 41. #4039 | D5 | semidirect |
| 47. #3941 | D5 | semidirect |
| 123. D20 | C4×D5 | semidirect |
| 124. D20 | C4×D5 | semidirect |
| 139. C52 | #442 | semidirect |
| 212. C5 | #65074 | semidirect |
| 213. C5 | #65303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| Dic5×D20 | 2 |
| C2×#87770 | 2 |
| #11716675 | 2 |
| C5×#3941 | 2 |
| #11716604 | 2 |
| #11716595 | 2 |
| #65303 | 5 |
| #65074 | 5 |