Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 102 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. C4⋊#6034 | C2 | semidirect |
| 4. C4×#6034 | C2 | semidirect |
| 15. C2×C4×C52 | C8 | semidirect |
| 65. C2×C4×C5 | #170 | semidirect |
| 85. C52 | #431 | semidirect |
| 129. C2×C4 | #6034 | semidirect |
| 134. C5 | #65748 | 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 |
| C4⋊#6034 | 2 |
| C4×#6034 | 2 |
| #65748 | 5 |