Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
582 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 17. #11716773 | C4 | semidirect |
| 22. C5×#3954 | C4 | semidirect |
| 23. #11716618 | C4 | semidirect |
| 98. #3954 | AGL(1,𝔽5) | semidirect |
| 212. C52 | #1778 | semidirect |
| 285. C5 | #10604086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×#1043 | 2 |
| #13103965 | 2 |
| C2×#11716763 | 2 |
| #13103905 | 2 |
| #13101153 | 2 |
| #13100372 | 2 |
| #13099909 | 2 |
| #10604086 | 5 |