Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1536 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 4. C2×C8×#1043 | C2 | semidirect |
| 5. #13100270 | C2 | semidirect |
| 10. C22×C52×C8 | C4 | semidirect |
| 11. C22×#6029 | C4 | semidirect |
| 13. C2×C8×C5⋊D5 | C4 | semidirect |
| 14. C2×C8×C5⋊D5 | C4 | semidirect |
| 17. C22⋊#6033 | C4 | semidirect |
| 19. #11716871 | C4 | semidirect |
| 32. C22⋊#1043 | C8 | direct (N × H) |
| 61. C2×#1043 | C2×C8 | semidirect |
| 77. C52×C8 | C22⋊C4 | semidirect |
| 79. #6029 | C22⋊C4 | semidirect |
| 84. C22×C5×C8 | AGL(1,𝔽5) | semidirect |
| 98. C22×C52 | C4×C8 | semidirect |
| 103. C2×C5⋊D5 | C4×C8 | semidirect |
| 174. C5×C8 | C22⋊AGL(1,𝔽5) | semidirect |
| 185. C22×C8 | #1043 | semidirect |
| 192. C52 | C8×C22⋊C4 | semidirect |
| 195. C22×C5 | C8×AGL(1,𝔽5) | semidirect |
| 268. C8 | C22⋊#1043 | direct (N × H) |
| 269. C5 | C8×C22⋊AGL(1,𝔽5) | semidirect |
| 279. C22 | C8×#1043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C5⋊D5 | 2 |
| C4×C22⋊#1043 | 2 |
| #13104762 | 2 |
| C2×C8×#1043 | 2 |
| #13100270 | 2 |
| C8×C22⋊AGL(1,𝔽5) | 5 |