Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2720 conjugacy classes of subgroups; only the 566 normal subgroups are shown.
This group has 2720 conjugacy classes of subgroups — too many to draw. Only its 566 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×#11716860 | C2 | direct (N × H) |
| 7. C22×#6033 | C4 | semidirect |
| 10. C2×#87855 | C4 | semidirect |
| 12. C22×C52×C8 | C4 | semidirect |
| 13. C22×#6029 | C4 | semidirect |
| 14. C2×C8×C5⋊D5 | C4 | semidirect |
| 16. #11716860 | C22 | direct (N × H) |
| 27. C2×#6033 | C2×C4 | semidirect |
| 30. #87855 | C2×C4 | semidirect |
| 32. C2×C52×C8 | C2×C4 | semidirect |
| 33. C2×#6029 | C2×C4 | semidirect |
| 34. C8×C5⋊D5 | C2×C4 | semidirect |
| 55. #6033 | C22×C4 | semidirect |
| 56. C52×C8 | C22×C4 | semidirect |
| 57. #6029 | C22×C4 | semidirect |
| 65. C22×C5×C8 | AGL(1,𝔽5) | semidirect |
| 71. C22×C52 | #97 | semidirect |
| 73. C2×C5⋊D5 | #97 | semidirect |
| 96. C2×C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 104. C2×C52 | C2×#97 | semidirect |
| 106. C5⋊D5 | C2×#97 | semidirect |
| 124. C5×C8 | C22×AGL(1,𝔽5) | semidirect |
| 134. C22×C8 | #1043 | semidirect |
| 138. C52 | C22×#97 | semidirect |
| 139. C22×C5 | #3992 | semidirect |
| 165. C2×C8 | C2×#1043 | semidirect |
| 168. C2×C5 | C2×#3992 | semidirect |
| 189. C8 | C22×#1043 | semidirect |
| 190. C5 | C22×#3992 | semidirect |
| 195. C22 | #11716860 | direct (N × H) |
| 204. C2 | C2×#11716860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#1043 | 2 |
| C22×#87855 | 2 |
| C22×C8×C5⋊D5 | 2 |
| C2×#11716860 | 2 |
| C22×#3992 | 5 |