Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 178 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. #11717454 | C2 | direct (N × H) |
| 3. C2×#87863 | C2 | semidirect |
| 4. C2×#87862 | C2 | semidirect |
| 12. #87863 | C22 | semidirect |
| 13. #87862 | C22 | semidirect |
| 50. C2×C52 | #131 | semidirect |
| 73. C52 | C2×#131 | semidirect |
| 97. C2×C5 | #4133 | semidirect |
| 111. C5 | C2×#4133 | semidirect |
| 119. C2 | #11717454 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87904 | 2 |
| #11717454 | 2 |
| C2×#87863 | 2 |
| C2×#87862 | 2 |
| C2×#4133 | 5 |