Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1120 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1120 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 9. C4×C52×C8 | C4 | semidirect |
| 10. C8×#1039 | C4 | semidirect |
| 11. C4×#6029 | C4 | semidirect |
| 38. C52×C8 | C4⋊C4 | semidirect |
| 39. #6029 | C4⋊C4 | semidirect |
| 45. C4×C5×C8 | AGL(1,𝔽5) | semidirect |
| 54. C4×C52 | #106 | semidirect |
| 56. #1039 | #106 | semidirect |
| 87. C5×C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 96. C4×C8 | #1043 | semidirect |
| 97. C52 | #1844 | semidirect |
| 103. C4×C5 | #3993 | semidirect |
| 134. C8 | C4⋊#1043 | semidirect |
| 135. C5 | #10603847 | semidirect |
| 143. C4 | #11716861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716861 | 2 |
| #13104700 | 2 |
| C4×C8×C5⋊D5 | 2 |
| #10603847 | 5 |