Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #11716897 | C2 | semidirect |
| 4. C4×#6034 | C2 | semidirect |
| 19. C2×#1039 | C8 | semidirect |
| 85. C52 | #431 | semidirect |
| 134. C5 | #65754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C22⋊#6034 | 2 |
| #11716897 | 2 |
| C4×#6034 | 2 |
| #65754 | 5 |