Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
718 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 98 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. #13107609 | C2 | semidirect |
| 3. #13104653 | C2 | semidirect |
| 4. C5×#65769 | C2 | semidirect |
| 5. #13103536 | C2 | semidirect |
| 6. #13099788 | C2 | semidirect |
| 7. #13099786 | C2 | semidirect |
| 17. #11717260 | C4 | semidirect |
| 18. C5×#4082 | C4 | semidirect |
| 22. #11716985 | C4 | semidirect |
| 23. #11716982 | C4 | semidirect |
| 52. #87849 | D4 | semidirect |
| 58. C5×#700 | D4 | semidirect |
| 74. #65769 | D5 | semidirect |
| 138. #4082 | AGL(1,𝔽5) | semidirect |
| 226. #700 | C22⋊D5 | semidirect |
| 368. C52 | #1884 | semidirect |
| 504. C5 | #10601210 | semidirect |
| 505. C5 | #10604569 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107609 | 2 |
| #13106294 | 2 |
| #13104653 | 2 |
| C5×#65769 | 2 |
| #13103536 | 2 |
| #13099788 | 2 |
| #13099786 | 2 |
| #10604569 | 5 |
| #10601210 | 5 |