Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2018 conjugacy classes of subgroups; only the 483 normal subgroups are shown.
This group has 2018 conjugacy classes of subgroups — too many to draw. Only its 483 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×#11716761 | C2 | direct (N × H) |
| 7. C22×#6034 | C4 | semidirect |
| 8. C2×#87862 | C4 | semidirect |
| 12. C22×C5×#168 | C4 | semidirect |
| 13. C2×#87767 | C4 | semidirect |
| 15. #11716761 | C22 | direct (N × H) |
| 18. C22×#1043 | C8 | semidirect |
| 26. C2×#6034 | C2×C4 | semidirect |
| 27. #87862 | C2×C4 | semidirect |
| 31. C2×C5×#168 | C2×C4 | semidirect |
| 32. #87767 | C2×C4 | semidirect |
| 43. C2×#1043 | C2×C8 | semidirect |
| 54. #6034 | C22×C4 | semidirect |
| 55. C5×#168 | C22×C4 | semidirect |
| 68. C22×#168 | AGL(1,𝔽5) | semidirect |
| 73. C22×C52 | C4×C8 | semidirect |
| 75. C2×C5⋊D5 | C4×C8 | semidirect |
| 79. #1043 | C22×C8 | semidirect |
| 110. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 117. C2×C52 | C2×C4×C8 | semidirect |
| 119. C5⋊D5 | C2×C4×C8 | semidirect |
| 153. #168 | C22×AGL(1,𝔽5) | semidirect |
| 165. C52 | C22×C4×C8 | semidirect |
| 168. C22×C5 | C8×AGL(1,𝔽5) | semidirect |
| 207. C2×C5 | C2×C8×AGL(1,𝔽5) | semidirect |
| 231. C5 | C22×C8×AGL(1,𝔽5) | semidirect |
| 236. C22 | #11716761 | direct (N × H) |
| 245. C2 | C2×#11716761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#87862 | 2 |
| C22×C4×#1043 | 2 |
| C22×#87767 | 2 |
| C2×#11716761 | 2 |
| C22×C8×AGL(1,𝔽5) | 5 |