Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
734 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 23. #11716782 | C4 | semidirect |
| 26. C5×#3956 | C4 | semidirect |
| 27. #11716601 | C4 | semidirect |
| 124. #3956 | AGL(1,𝔽5) | semidirect |
| 135. #1043 | #101 | semidirect |
| 270. C52 | C4×#101 | semidirect |
| 372. C5 | AGL(1,𝔽5)×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717353 | 2 |
| M16×#1043 | 2 |
| #13103928 | 2 |
| #13103905 | 2 |
| #13101184 | 2 |
| #13100369 | 2 |
| #13099913 | 2 |
| AGL(1,𝔽5)×#101 | 5 |