Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1784 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 1784 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 1. #13107245 | C2 | semidirect |
| 2. C52×#493 | C2 | semidirect |
| 3. #13103022 | C2 | semidirect |
| 4. #13103012 | C2 | semidirect |
| 5. #13102933 | C2 | semidirect |
| 6. C4×#87799 | C2 | semidirect |
| 7. #13102543 | C2 | semidirect |
| 46. C5×#493 | D5 | semidirect |
| 67. C52×C8 | #41 | semidirect |
| 119. #493 | C5⋊D5 | semidirect |
| 143. C5×C8 | #711 | semidirect |
| 161. C52 | #3184 | semidirect |
| 213. C8 | #87902 | semidirect |
| 214. C5 | #10613508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107245 | 2 |
| C52×#493 | 2 |
| #13103022 | 2 |
| #13103012 | 2 |
| #13102933 | 2 |
| C4×#87799 | 2 |
| #13102543 | 2 |
| #10613508 | 5 |