Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
298 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 2. #11716991 | C2 | semidirect |
| 5. #11716616 | C2 | semidirect |
| 6. #11716614 | C2 | semidirect |
| 7. #11716613 | C2 | semidirect |
| 130. C52 | #478 | semidirect |
| 198. C5 | #65052 | semidirect |
| 199. C5 | #65055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1039 | 2 |
| #11716991 | 2 |
| C5×#3964 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #11716613 | 2 |
| #65055 | 5 |
| #65052 | 5 |