Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
626 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 11. #11716887 | C4 | semidirect |
| 12. #11716886 | C4 | semidirect |
| 13. C8×#1043 | C4 | semidirect |
| 14. C8×#1043 | C4 | semidirect |
| 17. C5×#3951 | C4 | semidirect |
| 18. #11716619 | C4 | semidirect |
| 81. #3951 | AGL(1,𝔽5) | semidirect |
| 183. C52 | #1772 | semidirect |
| 249. C5 | #10604089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104859 | 2 |
| C2×C8×#1043 | 2 |
| #13103902 | 2 |
| #13101043 | 2 |
| #13099900 | 2 |
| #10604089 | 5 |