Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1784 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 1784 conjugacy classes of subgroups — too many to draw. Only its 295 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. #13107254 | C2 | semidirect |
| 2. #13107245 | C2 | semidirect |
| 3. C52×#486 | C2 | semidirect |
| 4. #13102942 | C2 | semidirect |
| 5. #13102935 | C2 | semidirect |
| 6. #13102647 | C2 | semidirect |
| 7. #13102644 | C2 | semidirect |
| 8. #13102557 | C2 | semidirect |
| 9. C4×#87799 | C2 | semidirect |
| 71. C5×#486 | D5 | semidirect |
| 105. #6029 | #41 | semidirect |
| 188. #486 | C5⋊D5 | semidirect |
| 251. C52 | #3184 | semidirect |
| 337. C5 | #10613291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107254 | 2 |
| #13107245 | 2 |
| C52×#486 | 2 |
| #13102942 | 2 |
| #13102935 | 2 |
| #13102647 | 2 |
| #13102644 | 2 |
| #13102557 | 2 |
| C4×#87799 | 2 |
| #10613291 | 5 |