Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
746 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 12. C4×C5×#168 | C4 | semidirect |
| 13. #11716594 | C4 | semidirect |
| 47. C5×#168 | C4⋊C4 | semidirect |
| 60. C4×#168 | AGL(1,𝔽5) | semidirect |
| 69. C4×C52 | #107 | semidirect |
| 71. #1039 | #107 | semidirect |
| 130. #168 | C4⋊AGL(1,𝔽5) | semidirect |
| 140. C52 | #1845 | semidirect |
| 156. C4×C5 | #3994 | semidirect |
| 201. C5 | #10603848 | semidirect |
| 211. C4 | #11716772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104826 | 2 |
| #13104700 | 2 |
| C2×#11716772 | 2 |
| C4×#87767 | 2 |
| #10603848 | 5 |