Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
276 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 54 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×#87810 | C2 | semidirect |
| 3. #11716949 | C2 | semidirect |
| 4. #11716933 | C2 | semidirect |
| 5. C5×#3965 | C2 | semidirect |
| 6. #11716619 | C2 | semidirect |
| 7. #11716602 | C2 | semidirect |
| 51. #3965 | D5 | semidirect |
| 152. C52 | #471 | semidirect |
| 218. C5 | #65037 | semidirect |
| 219. C5 | #65489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87810 | 2 |
| C5×#4078 | 2 |
| #11716949 | 2 |
| #11716933 | 2 |
| C5×#3965 | 2 |
| #11716619 | 2 |
| #11716602 | 2 |
| #65489 | 5 |
| #65037 | 5 |