Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
688 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 208 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. #11716985 | C2 | direct (N × H) |
| 16. C2×#1039 | Q8 | semidirect |
| 31. #1039 | C2×Q8 | semidirect |
| 47. C2×C52 | C4⋊Q8 | semidirect |
| 70. C52 | C2×C4⋊Q8 | semidirect |
| 93. C2×C5 | #4090 | semidirect |
| 105. C5 | C2×#4090 | semidirect |
| 112. C2 | #11716985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C2×C4×#1039 | 2 |
| C2×#87781 | 2 |
| #11716985 | 2 |
| C2×#4090 | 5 |