Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 4. #11716689 | C2 | semidirect |
| 5. C5×#3954 | C2 | semidirect |
| 6. #11716619 | C2 | semidirect |
| 7. #11716618 | C2 | semidirect |
| 49. #3954 | D5 | semidirect |
| 130. C52 | #430 | semidirect |
| 187. C5 | #65182 | semidirect |
| 188. C5 | #65413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×M16 | 2 |
| C2×#87768 | 2 |
| D5×#681 | 2 |
| #11716689 | 2 |
| C5×#3954 | 2 |
| #11716619 | 2 |
| #11716618 | 2 |
| #65413 | 5 |
| #65182 | 5 |