Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 356 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. C2×#87811 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. #11717029 | C2 | semidirect |
| 5. C2×#87771 | C2 | semidirect |
| 6. C2×#87770 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 38. #6029 | D4 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 42. #4093 | D5 | semidirect |
| 46. C2×#688 | D5 | semidirect |
| 143. #168 | C22⋊D5 | semidirect |
| 151. C52 | #496 | semidirect |
| 224. C5 | #65347 | semidirect |
| 225. C5 | #65465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87811 | 2 |
| C5×#4093 | 2 |
| C2×C5×#688 | 2 |
| #11717029 | 2 |
| C2×#87771 | 2 |
| C2×#87770 | 2 |
| #11716595 | 2 |
| #65465 | 5 |
| #65347 | 5 |