Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
992 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 166 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×#106 | C4 | semidirect |
| 16. #11716684 | C4 | semidirect |
| 17. #11716675 | C4 | semidirect |
| 61. C52×C8 | C4⋊C4 | semidirect |
| 62. #6029 | C4⋊C4 | semidirect |
| 72. C5×#106 | AGL(1,𝔽5) | semidirect |
| 136. C5×C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 147. #106 | #1043 | semidirect |
| 150. C52 | #1941 | semidirect |
| 207. C8 | C4⋊#1043 | semidirect |
| 208. C5 | #10604051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716861 | 2 |
| C2×C8×#1043 | 2 |
| #13104724 | 2 |
| #106×C5⋊D5 | 2 |
| #13100253 | 2 |
| #10604051 | 5 |