Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
890 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4⋊C4×#1044 | C2 | semidirect |
| 4. C2×#11716764 | C2 | semidirect |
| 6. #13100253 | C2 | semidirect |
| 7. #13099908 | C2 | semidirect |
| 17. #11717365 | C4 | semidirect |
| 21. #11716766 | C4 | semidirect |
| 23. C5×#3941 | C4 | semidirect |
| 24. #11716604 | C4 | semidirect |
| 43. C4⋊#1044 | C2×C4 | semidirect |
| 51. #87855 | C2×C4 | semidirect |
| 53. C52×C4⋊C4 | C2×C4 | semidirect |
| 54. C4⋊#1039 | C2×C4 | semidirect |
| 56. C2×C5×#168 | C2×C4 | semidirect |
| 99. C5×D20 | C42 | semidirect |
| 125. #3941 | AGL(1,𝔽5) | semidirect |
| 189. C5×C4⋊C4 | C2×AGL(1,𝔽5) | semidirect |
| 194. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 251. D20 | C4×AGL(1,𝔽5) | semidirect |
| 285. C52 | #1762 | semidirect |
| 355. C4⋊C4 | D5⋊AGL(1,𝔽5) | semidirect |
| 414. C5 | #10603952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717365 | 2 |
| C4⋊C4×#1044 | 2 |
| C2×#11716766 | 2 |
| C2×#11716764 | 2 |
| #13100774 | 2 |
| #13100253 | 2 |
| #13099908 | 2 |
| #10603952 | 5 |