Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
230 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 230 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. #11717224 | C2 | semidirect |
| 2. C5×#4050 | C2 | semidirect |
| 3. C2×C5×#672 | C2 | semidirect |
| 4. #11716592 | C2 | semidirect |
| 5. #11716590 | C2 | semidirect |
| 6. #11716589 | C2 | semidirect |
| 7. #11716587 | C2 | semidirect |
| 36. #4050 | D5 | semidirect |
| 42. C2×#672 | D5 | semidirect |
| 122. C52 | #508 | semidirect |
| 176. C5 | #65193 | semidirect |
| 177. C5 | #65483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717224 | 2 |
| C5×#4050 | 2 |
| C2×C5×#672 | 2 |
| #11716592 | 2 |
| #11716590 | 2 |
| #11716589 | 2 |
| #11716587 | 2 |
| #65483 | 5 |
| #65193 | 5 |