Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
640 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 138 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×#6034 | C2 | semidirect |
| 3. C22⋊#6034 | C2 | direct (N × H) |
| 11. C2×#6034 | C22 | semidirect |
| 15. C23×C52 | C8 | semidirect |
| 35. C22×C52 | C2×C8 | semidirect |
| 57. C2×C52 | C22⋊C8 | semidirect |
| 68. C23×C5 | #170 | semidirect |
| 89. C52 | C2×C22⋊C8 | semidirect |
| 102. C22×C5 | C2×#170 | semidirect |
| 126. C2×C5 | C22⋊#170 | semidirect |
| 132. C23 | #6034 | semidirect |
| 144. C5 | C2×C22⋊#170 | semidirect |
| 149. C22 | C2×#6034 | semidirect |
| 157. C2 | C22⋊#6034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C22×#6034 | 2 |
| C22⋊#6034 | 2 |
| C2×C22⋊#170 | 5 |