Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
396 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11717260 | C2 | semidirect |
| 2. C2×C5×#687 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. #11716981 | C2 | semidirect |
| 5. C2×#87774 | C2 | semidirect |
| 6. C2×#87771 | C2 | semidirect |
| 7. #11716596 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 48. C2×#687 | D5 | semidirect |
| 50. C2×#686 | D5 | semidirect |
| 143. #168 | C22⋊D5 | semidirect |
| 144. #168 | C22⋊D5 | semidirect |
| 152. C52 | #496 | semidirect |
| 228. C5 | #65443 | semidirect |
| 229. C5 | #65465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717260 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×#686 | 2 |
| #11716981 | 2 |
| C2×#87774 | 2 |
| C2×#87771 | 2 |
| #11716596 | 2 |
| #65465 | 5 |
| #65443 | 5 |