Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
452 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#87839 | C2 | semidirect |
| 4. #11717386 | C2 | direct (N × H) |
| 13. #87839 | C22 | semidirect |
| 28. C2×C5⋊D5 | Q16 | semidirect |
| 45. C2×C52 | C2×Q16 | semidirect |
| 47. C5⋊D5 | C2×Q16 | semidirect |
| 70. C52 | C22×Q16 | semidirect |
| 121. C2 | #11717386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87872 | 2 |
| C2×#87862 | 2 |
| C2×#87839 | 2 |
| #11717386 | 2 |
| C22×Q16 | 25 |