Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
978 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #13103985 | C2 | semidirect |
| 4. C2×#11716764 | C2 | semidirect |
| 6. #13099908 | C2 | semidirect |
| 7. #13099907 | C2 | semidirect |
| 12. D4×#1044 | C4 | semidirect |
| 20. #11716875 | C4 | semidirect |
| 23. C5×#3964 | C4 | semidirect |
| 24. #11716605 | C4 | semidirect |
| 50. C4⋊#1043 | C2×C4 | semidirect |
| 52. #87855 | C2×C4 | semidirect |
| 54. C5×C4⋊Dic5 | C2×C4 | semidirect |
| 55. C2×C5×#168 | C2×C4 | semidirect |
| 90. C52×D4 | C42 | semidirect |
| 96. C4⋊(C5⋊D5) | C42 | semidirect |
| 126. #3964 | AGL(1,𝔽5) | semidirect |
| 201. C4⋊Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 203. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 259. C5×D4 | C4×AGL(1,𝔽5) | semidirect |
| 305. C52 | #1762 | semidirect |
| 420. D4 | #87830 | semidirect |
| 446. C5 | #10603952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1044 | 2 |
| C2×#11716875 | 2 |
| #13103985 | 2 |
| C2×#11716764 | 2 |
| #13101587 | 2 |
| #13099908 | 2 |
| #13099907 | 2 |
| #10603952 | 5 |