Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
246 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 56 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×#4053 | C2 | semidirect |
| 2. #11716949 | C2 | semidirect |
| 3. C2×#87773 | C2 | semidirect |
| 5. #11716691 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. #11716618 | C2 | semidirect |
| 47. #4053 | D5 | semidirect |
| 53. #3955 | D5 | semidirect |
| 147. C52 | #471 | semidirect |
| 210. C5 | #65037 | semidirect |
| 211. C5 | #65430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4053 | 2 |
| #11716949 | 2 |
| C2×#87773 | 2 |
| #11716941 | 2 |
| #11716691 | 2 |
| C5×#3955 | 2 |
| #11716618 | 2 |
| #65430 | 5 |
| #65037 | 5 |