Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 74 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×#87809 | C2 | semidirect |
| 2. C5×#4086 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. #11717029 | C2 | semidirect |
| 5. C2×#87771 | C2 | semidirect |
| 6. C2×#87770 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 39. #6029 | D4 | semidirect |
| 40. C5×#168 | D4 | semidirect |
| 44. #4086 | D5 | semidirect |
| 51. C2×#686 | D5 | semidirect |
| 67. C5×Dic5 | D8 | semidirect |
| 148. #168 | C22⋊D5 | semidirect |
| 156. C52 | #493 | semidirect |
| 187. Dic5 | #686 | semidirect |
| 236. C5 | #65362 | semidirect |
| 237. C5 | #65440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87809 | 2 |
| C5×#4086 | 2 |
| C2×C5×#686 | 2 |
| #11717029 | 2 |
| C2×#87771 | 2 |
| C2×#87770 | 2 |
| Dic5×#168 | 2 |
| #65440 | 5 |
| #65362 | 5 |