Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1858 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1858 conjugacy classes of subgroups — too many to draw. Only its 403 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×#11716763 | 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. #11716763 | C22 | direct (N × H) |
| 26. C2×#6034 | C2×C4 | semidirect |
| 27. #87862 | C2×C4 | semidirect |
| 31. C2×C5×#168 | C2×C4 | semidirect |
| 32. #87767 | C2×C4 | semidirect |
| 54. #6034 | C22×C4 | semidirect |
| 55. C5×#168 | C22×C4 | semidirect |
| 68. C22×#168 | AGL(1,𝔽5) | semidirect |
| 73. C22×C52 | #97 | semidirect |
| 75. C2×C5⋊D5 | #97 | semidirect |
| 111. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 118. C2×C52 | C2×#97 | semidirect |
| 120. C5⋊D5 | C2×#97 | semidirect |
| 155. #168 | C22×AGL(1,𝔽5) | semidirect |
| 167. C52 | C22×#97 | semidirect |
| 170. C22×C5 | #3992 | semidirect |
| 210. C2×C5 | C2×#3992 | semidirect |
| 234. C5 | C22×#3992 | semidirect |
| 239. C22 | #11716763 | direct (N × H) |
| 248. C2 | C2×#11716763 | 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×#11716763 | 2 |
| C22×#3992 | 5 |