Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
718 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 117 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. #13107786 | C2 | semidirect |
| 3. #13104655 | C2 | semidirect |
| 4. #13104653 | C2 | semidirect |
| 5. #13100146 | C2 | semidirect |
| 12. C52×#127 | C4 | semidirect |
| 14. C5×#4082 | C4 | semidirect |
| 15. C5×#4082 | C4 | semidirect |
| 18. C5×#4015 | C4 | semidirect |
| 44. #87849 | D4 | semidirect |
| 97. C5×#127 | Dic5 | semidirect |
| 98. C5×#127 | AGL(1,𝔽5) | semidirect |
| 106. #4082 | Dic5 | semidirect |
| 107. #4082 | Dic5 | semidirect |
| 113. #4015 | Dic5 | semidirect |
| 269. #127 | #1042 | semidirect |
| 278. C52 | #1884 | semidirect |
| 385. C5 | #10602610 | semidirect |
| 386. C5 | #10604618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107786 | 2 |
| C5×#66050 | 2 |
| #13104655 | 2 |
| #13104653 | 2 |
| #13100146 | 2 |
| #10604618 | 5 |
| #10602610 | 5 |