Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
626 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 103 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. C5×#3949 | C4 | semidirect |
| 16. #11716615 | C4 | semidirect |
| 61. C52×C8 | C4⋊C4 | semidirect |
| 62. #6029 | C4⋊C4 | semidirect |
| 78. #3949 | AGL(1,𝔽5) | semidirect |
| 175. C5×C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 189. C52 | #1944 | semidirect |
| 265. C8 | #87832 | semidirect |
| 267. C5 | #10604052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716887 | 2 |
| C2×#11716860 | 2 |
| #13104001 | 2 |
| #13100851 | 2 |
| #13099907 | 2 |
| #10604052 | 5 |