Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 144 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. #11716613 | C2 | direct (N × H) |
| 18. C2×#1039 | C8 | semidirect |
| 35. #1039 | C2×C8 | semidirect |
| 51. C2×C52 | C4⋊C8 | semidirect |
| 78. C52 | C2×C4⋊C8 | semidirect |
| 108. C2×C5 | #3946 | semidirect |
| 123. C5 | C2×#3946 | semidirect |
| 133. C2 | #11716613 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C22×C5×#168 | 2 |
| #11716613 | 2 |
| C2×#3946 | 5 |