Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
638 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 106 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. #11716848 | C4 | semidirect |
| 18. C5×#4005 | C4 | semidirect |
| 19. #11716758 | C4 | semidirect |
| 88. #4005 | AGL(1,𝔽5) | semidirect |
| 102. #1044 | #101 | semidirect |
| 206. C52 | C4×#101 | semidirect |
| 291. 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×#11717355 | 2 |
| #13107464 | 2 |
| #13103695 | 2 |
| #13103287 | 2 |
| AGL(1,𝔽5)×#101 | 5 |