Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1328 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 206 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 |
|---|---|---|
| 9. C52×C4⋊Q8 | C4 | semidirect |
| 10. #11717264 | C4 | semidirect |
| 14. #11717189 | C4 | semidirect |
| 65. C5×C4⋊Q8 | AGL(1,𝔽5) | semidirect |
| 81. C4×C52 | #103 | semidirect |
| 84. #1039 | #103 | semidirect |
| 139. C4⋊Q8 | #1043 | semidirect |
| 146. C52 | #1956 | semidirect |
| 154. C4×C5 | #4009 | semidirect |
| 203. C5 | #10604672 | semidirect |
| 214. C4 | #11716877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×C5⋊D5 | 2 |
| C2×#11716877 | 2 |
| #13104700 | 2 |
| C4×#87855 | 2 |
| #10604672 | 5 |