Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
810 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13103904 | C2 | semidirect |
| 4. #13103879 | C2 | semidirect |
| 6. #13099904 | C2 | semidirect |
| 7. #13099900 | C2 | semidirect |
| 9. Q8×#1044 | C4 | semidirect |
| 11. D4×#1044 | C4 | semidirect |
| 20. #11716878 | C4 | semidirect |
| 21. #11716876 | C4 | semidirect |
| 25. C5×#3969 | C4 | semidirect |
| 26. #11716611 | C4 | semidirect |
| 54. C4×#1043 | C2×C4 | semidirect |
| 55. #87856 | C2×C4 | semidirect |
| 57. C4×C5×Dic5 | C2×C4 | semidirect |
| 58. C5×#681 | C2×C4 | semidirect |
| 127. #3969 | AGL(1,𝔽5) | semidirect |
| 198. C4×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 199. #681 | C2×AGL(1,𝔽5) | semidirect |
| 296. C52 | #1759 | semidirect |
| 411. C5 | #10604002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#1044 | 2 |
| #13104804 | 2 |
| #13103904 | 2 |
| #13103879 | 2 |
| #13101844 | 2 |
| #13099904 | 2 |
| #13099900 | 2 |
| #10604002 | 5 |