Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
2178 conjugacy classes of subgroups; only the 414 normal subgroups are shown.
This group has 2178 conjugacy classes of subgroups — too many to draw. Only its 414 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. #13104824 | C2 | direct (N × H) |
| 8. C2×C4×#1044 | C4 | semidirect |
| 10. C2×C42×C52 | C4 | semidirect |
| 11. C2×C4×#1039 | C4 | semidirect |
| 12. C2×C4×#1039 | C4 | semidirect |
| 13. C42×C5⋊D5 | C4 | semidirect |
| 31. C4×#1044 | C2×C4 | semidirect |
| 32. C42×C52 | C2×C4 | semidirect |
| 33. C4×#1039 | C2×C4 | semidirect |
| 34. C4×#1039 | C2×C4 | semidirect |
| 68. C2×C42×C5 | AGL(1,𝔽5) | semidirect |
| 120. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 129. C2×C52 | #376 | semidirect |
| 132. C5⋊D5 | #376 | semidirect |
| 184. C2×C42 | #1044 | semidirect |
| 186. C52 | C2×#376 | semidirect |
| 231. C42 | C2×#1044 | semidirect |
| 235. C2×C5 | #65686 | semidirect |
| 263. C5 | C2×#65686 | semidirect |
| 279. C2 | #13104824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#1044 | 2 |
| C2×C42×C5⋊D5 | 2 |
| C2×#11716899 | 2 |
| #13104824 | 2 |
| C2×#65686 | 5 |