Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 4. #11716675 | C2 | semidirect |
| 5. C5×#3939 | C2 | semidirect |
| 6. #11716616 | C2 | semidirect |
| 7. #11716615 | C2 | semidirect |
| 19. D5×#168 | C4 | semidirect |
| 47. #3939 | D5 | semidirect |
| 124. C52 | #427 | semidirect |
| 187. C5 | #65169 | semidirect |
| 188. C5 | #65287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4038 | 2 |
| #11716959 | 2 |
| C2×D5×#168 | 2 |
| #11716675 | 2 |
| C5×#3939 | 2 |
| #11716616 | 2 |
| #11716615 | 2 |
| #65287 | 5 |
| #65169 | 5 |