Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 142 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. C2×C5×#681 | C2 | semidirect |
| 3. C5×#3965 | C2 | direct (N × H) |
| 11. C5×#681 | C22 | semidirect |
| 14. C2×#3965 | C5 | direct (N × H) |
| 31. C2×#681 | C2×C5 | semidirect |
| 33. #3965 | C2×C5 | direct (N × H) |
| 66. #681 | C22×C5 | semidirect |
| 72. C2×C52 | #100 | semidirect |
| 112. C52 | C2×#100 | semidirect |
| 163. C2×C5 | #3965 | direct (N × H) |
| 164. C2×C5 | C5×#100 | semidirect |
| 180. C5 | C2×#3965 | direct (N × H) |
| 181. C5 | C2×C5×#100 | semidirect |
| 195. C2 | C5×#3965 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×#681 | 2 |
| C5×#3965 | 2 |
| C2×C5×#100 | 5 |
| C2×#3965 | 5 |