Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
3968 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 3968 conjugacy classes of subgroups — too many to draw. Only its 390 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×#11717435 | C2 | semidirect |
| 3. C2×#11716881 | C2 | semidirect |
| 4. #13104790 | C2 | direct (N × H) |
| 15. C2×#87860 | C22 | semidirect |
| 17. #11717435 | C22 | semidirect |
| 20. #11716881 | C22 | semidirect |
| 52. #87860 | C23 | semidirect |
| 130. C2×C5⋊D5 | #100 | semidirect |
| 177. C2×C52 | C2×#100 | semidirect |
| 181. C5⋊D5 | C2×#100 | semidirect |
| 234. C52 | C22×#100 | semidirect |
| 295. C2×C5 | D5⋊#100 | semidirect |
| 336. C5 | C2×D5⋊#100 | semidirect |
| 366. C2 | #13104790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C5⋊D5 | 2 |
| C2×#11717435 | 2 |
| C2×#11716881 | 2 |
| #13104790 | 2 |
| C2×D5⋊#100 | 5 |