Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
698 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 123 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×#3935 | C4 | semidirect |
| 16. #11716596 | C4 | semidirect |
| 55. C5×#168 | C4⋊C4 | semidirect |
| 70. #3935 | AGL(1,𝔽5) | semidirect |
| 147. #168 | C4⋊AGL(1,𝔽5) | semidirect |
| 159. C52 | #1847 | semidirect |
| 225. C5 | #10603883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104827 | 2 |
| #13104700 | 2 |
| C2×#11716772 | 2 |
| C2×#11716771 | 2 |
| #13100501 | 2 |
| #10603883 | 5 |