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. #13107254 | C2 | semidirect |
| 2. C52×#498 | C2 | semidirect |
| 3. #13102952 | C2 | semidirect |
| 4. #13102732 | C2 | semidirect |
| 5. #13102729 | C2 | semidirect |
| 6. #13102558 | C2 | semidirect |
| 7. C4×#87799 | C2 | semidirect |
| 46. C5×#498 | D5 | semidirect |
| 67. C52×C8 | #41 | semidirect |
| 118. #498 | C5⋊D5 | semidirect |
| 143. C5×C8 | #713 | semidirect |
| 161. C52 | #3184 | semidirect |
| 213. C8 | #87904 | semidirect |
| 214. C5 | #10613619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107254 | 2 |
| C52×#498 | 2 |
| #13102952 | 2 |
| #13102732 | 2 |
| #13102729 | 2 |
| #13102558 | 2 |
| C4×#87799 | 2 |
| #10613619 | 5 |