Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1744 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1744 conjugacy classes of subgroups — too many to draw. Only its 232 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 |
|---|---|---|
| 3. C2×C8×#1043 | C2 | semidirect |
| 5. #13100270 | C2 | semidirect |
| 14. C22⋊#6033 | C4 | semidirect |
| 15. #11716871 | C4 | semidirect |
| 17. C52×C22⋊C8 | C4 | semidirect |
| 18. C22⋊#6029 | C4 | semidirect |
| 19. #11716687 | C4 | semidirect |
| 24. C22×#1043 | C8 | semidirect |
| 35. C2×#6033 | C2×C4 | semidirect |
| 41. C2×C52×C8 | C2×C4 | semidirect |
| 42. C2×#6029 | C2×C4 | semidirect |
| 90. C5×C22⋊C8 | AGL(1,𝔽5) | semidirect |
| 96. C22×C52 | C4×C8 | semidirect |
| 102. C2×C5⋊D5 | C4×C8 | semidirect |
| 108. #1043 | C22⋊C8 | direct (N × H) |
| 133. C2×C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 190. C22⋊C8 | #1043 | direct (N × H) |
| 192. C52 | C4×C22⋊C8 | semidirect |
| 195. C22×C5 | C8×AGL(1,𝔽5) | semidirect |
| 232. C2×C8 | C2×#1043 | semidirect |
| 272. C5 | AGL(1,𝔽5)×C22⋊C8 | semidirect |
| 284. C22 | C8×#1043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#1043 | 2 |
| #13104762 | 2 |
| C2×C8×#1043 | 2 |
| C22⋊C8×C5⋊D5 | 2 |
| #13100270 | 2 |
| AGL(1,𝔽5)×C22⋊C8 | 5 |