Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 308 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×#87812 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. #11716983 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 46. C2×#689 | D5 | semidirect |
| 144. C52 | #497 | semidirect |
| 206. C5 | #65349 | semidirect |
| 207. C5 | #65479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87812 | 2 |
| C5×#4093 | 2 |
| C2×C5×#689 | 2 |
| #11716983 | 2 |
| C2×#87773 | 2 |
| C2×#87772 | 2 |
| #11716595 | 2 |
| #65479 | 5 |
| #65349 | 5 |