Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1168 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 144 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. C2×C8×#1043 | C2 | semidirect |
| 4. #13104724 | C2 | semidirect |
| 6. #13100271 | C2 | semidirect |
| 7. #13100253 | C2 | semidirect |
| 21. C52×#102 | C4 | semidirect |
| 22. #11716699 | C4 | semidirect |
| 23. #11716688 | C4 | semidirect |
| 24. #11716676 | C4 | semidirect |
| 119. C5×#102 | AGL(1,𝔽5) | semidirect |
| 254. #102 | #1043 | semidirect |
| 257. C52 | #1934 | semidirect |
| 367. C5 | #10603963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104792 | 2 |
| C2×#11716875 | 2 |
| C2×C8×#1043 | 2 |
| #13104724 | 2 |
| #102×C5⋊D5 | 2 |
| #13100271 | 2 |
| #13100253 | 2 |
| #10603963 | 5 |