Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
196 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11716891 | C2 | semidirect |
| 3. C2×#87764 | C2 | semidirect |
| 4. #11716775 | C2 | semidirect |
| 5. D5⋊#674 | C2 | semidirect |
| 87. C52 | #504 | semidirect |
| 126. C5 | #65725 | semidirect |
| 127. C5 | #65791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716933 | 2 |
| #11716891 | 2 |
| C2×#87764 | 2 |
| #11716775 | 2 |
| D5⋊#674 | 2 |
| #65791 | 5 |
| #65725 | 5 |