Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
368 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 4. #11716778 | C2 | direct (N × H) |
| 7. C2×#6034 | C4 | semidirect |
| 9. C2×#6033 | C4 | semidirect |
| 21. #6034 | C2×C4 | semidirect |
| 22. #6033 | C2×C4 | semidirect |
| 48. C2×C52 | #97 | semidirect |
| 72. C52 | C2×#97 | semidirect |
| 99. C2×C5 | #4002 | semidirect |
| 113. C5 | C2×#4002 | semidirect |
| 121. C2 | #11716778 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C22×#6033 | 2 |
| C2×Dic52 | 2 |
| #11716778 | 2 |
| C2×#4002 | 5 |