Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1024 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 15. C52×#97 | C4 | semidirect |
| 16. #11716682 | C4 | semidirect |
| 17. #11716670 | C4 | semidirect |
| 56. C52×C8 | C4⋊C4 | semidirect |
| 57. #6029 | C4⋊C4 | semidirect |
| 67. C5×#97 | AGL(1,𝔽5) | semidirect |
| 125. C5×C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 137. #97 | #1043 | semidirect |
| 139. C52 | #1847 | semidirect |
| 190. C8 | C4⋊#1043 | semidirect |
| 191. C5 | #10603883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716862 | 2 |
| C2×#11716861 | 2 |
| #13104701 | 2 |
| #13104700 | 2 |
| #97×C5⋊D5 | 2 |
| #10603883 | 5 |