Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1386 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 236 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 |
|---|---|---|
| 1. C2×D4×#1035 | C2 | semidirect |
| 3. #13098769 | C2 | semidirect |
| 4. #13098677 | C2 | semidirect |
| 5. C42×#1035 | C2 | semidirect |
| 13. C25×#127 | C4 | semidirect |
| 14. #11716502 | C4 | semidirect |
| 15. #11716436 | C4 | semidirect |
| 23. C2×D4×C25 | C2×C4 | semidirect |
| 24. C2×C22⋊D25 | C2×C4 | semidirect |
| 27. C2×D100 | C2×C4 | semidirect |
| 32. C4×#1035 | D4 | semidirect |
| 33. C42×C25 | C2×C4 | semidirect |
| 34. C4×Dic25 | C2×C4 | semidirect |
| 78. #1035 | #127 | direct (N × H) |
| 79. C4×C25 | C4×D4 | semidirect |
| 80. Dic25 | C4×D4 | semidirect |
| 129. #127 | #1035 | direct (N × H) |
| 136. C25 | C4×#127 | semidirect |
| 154. C2×D4 | C2×#1035 | semidirect |
| 165. C42 | C2×#1035 | semidirect |
| 200. C4 | D4×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1035 | 2 |
| #127×D25 | 2 |
| #13098769 | 2 |
| #13098677 | 2 |
| C42×#1035 | 2 |
| AGL(1,𝔽5)×#127 | 5 |