Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1288 conjugacy classes of subgroups; only the 419 normal subgroups are shown.
This group has 1288 conjugacy classes of subgroups — too many to draw. Only its 419 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 |
|---|---|---|
| 2. C22×#6045 | C2 | semidirect |
| 4. C2×C4⋊#1039 | C2 | semidirect |
| 5. #11717244 | C2 | direct (N × H) |
| 6. C2×#87806 | C2 | semidirect |
| 15. C2×#6045 | C22 | semidirect |
| 17. C4⋊#1039 | C22 | semidirect |
| 18. #87806 | C22 | semidirect |
| 22. C23×C52 | Q8 | semidirect |
| 46. C22×C52 | C2×Q8 | semidirect |
| 67. C2×C52 | C22⋊Q8 | semidirect |
| 73. C23×C5 | Dic10 | semidirect |
| 92. C52 | C2×C22⋊Q8 | semidirect |
| 97. C22×C5 | C2×Dic10 | semidirect |
| 118. C2×C5 | #4070 | semidirect |
| 124. C23 | #6045 | semidirect |
| 137. C5 | C2×#4070 | semidirect |
| 142. C22 | C2×#6045 | semidirect |
| 151. C2 | #11717244 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C22×#6045 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×C4⋊#1039 | 2 |
| #11717244 | 2 |
| C2×#87806 | 2 |
| C2×#4070 | 5 |