Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
742 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 742 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. #13104657 | C2 | semidirect |
| 4. C5×#65767 | C2 | semidirect |
| 5. #13103536 | C2 | semidirect |
| 6. #13099782 | C2 | semidirect |
| 7. #13099780 | C2 | semidirect |
| 17. #11717260 | C4 | semidirect |
| 18. C5×#4082 | C4 | semidirect |
| 21. #11717029 | C4 | semidirect |
| 22. #11716981 | C4 | semidirect |
| 53. D5⋊#168 | D4 | semidirect |
| 59. C5×D5⋊C8 | D4 | semidirect |
| 74. #65767 | D5 | semidirect |
| 140. #4082 | AGL(1,𝔽5) | semidirect |
| 233. D5⋊C8 | C22⋊D5 | semidirect |
| 375. C52 | #1910 | semidirect |
| 520. C5 | #10601123 | semidirect |
| 521. C5 | #10604571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107609 | 2 |
| #13106293 | 2 |
| #13104657 | 2 |
| C5×#65767 | 2 |
| #13103536 | 2 |
| #13099782 | 2 |
| #13099780 | 2 |
| #10604571 | 5 |
| #10601123 | 5 |