Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
718 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 110 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. C5×#66256 | C2 | semidirect |
| 3. #13104655 | C2 | semidirect |
| 4. #13103561 | C2 | semidirect |
| 5. #13099788 | C2 | semidirect |
| 12. #11717260 | C4 | semidirect |
| 13. C5×#4082 | C4 | semidirect |
| 17. #11716985 | C4 | semidirect |
| 18. #11716982 | C4 | semidirect |
| 44. C5×#700 | D4 | semidirect |
| 52. #66256 | D5 | semidirect |
| 106. #4082 | AGL(1,𝔽5) | semidirect |
| 173. #700 | C22⋊D5 | semidirect |
| 278. C52 | #1884 | semidirect |
| 385. C5 | #10602814 | semidirect |
| 386. C5 | #10604568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#66256 | 2 |
| #13106294 | 2 |
| #13104655 | 2 |
| #13103561 | 2 |
| #13099788 | 2 |
| #10604568 | 5 |
| #10602814 | 5 |