Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
4416 conjugacy classes of subgroups; only the 390 normal subgroups are shown.
This group has 4416 conjugacy classes of subgroups — too many to draw. Only its 390 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. C2×#11717438 | C2 | semidirect |
| 3. #13104812 | C2 | semidirect |
| 4. #13104792 | C2 | semidirect |
| 6. C22×C52×D4 | C4 | semidirect |
| 7. C22×C22⋊(C5⋊D5) | C4 | semidirect |
| 9. C2×D4×C5⋊D5 | C4 | semidirect |
| 11. C22×C4⋊(C5⋊D5) | C4 | semidirect |
| 14. C2×C22⋊#1043 | C22 | semidirect |
| 16. C2×C4⋊#1043 | C22 | semidirect |
| 17. C2×C4×#1043 | C22 | semidirect |
| 68. C2×C4×C52 | C22⋊C4 | semidirect |
| 71. C2×#1039 | C22⋊C4 | semidirect |
| 74. C4×C5⋊D5 | C22⋊C4 | semidirect |
| 78. C22×C5×D4 | AGL(1,𝔽5) | semidirect |
| 166. C2×C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 181. C22×D4 | #1043 | semidirect |
| 188. C52 | #2309 | semidirect |
| 267. C2×C4 | C22⋊#1043 | semidirect |
| 269. C5 | #10617507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C5⋊D5 | 2 |
| C2×#11717438 | 2 |
| #13104812 | 2 |
| #13104792 | 2 |
| #10617507 | 5 |