Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1648 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 1648 conjugacy classes of subgroups — too many to draw. Only its 162 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×#11717435 | C2 | semidirect |
| 3. C2×#11716875 | C2 | semidirect |
| 4. #13104777 | C2 | semidirect |
| 5. #13100253 | C2 | semidirect |
| 15. C52×#121 | C4 | semidirect |
| 17. #11717258 | C4 | semidirect |
| 18. #11717250 | C4 | semidirect |
| 19. #11717215 | C4 | semidirect |
| 55. #87855 | D4 | semidirect |
| 118. C5×#121 | AGL(1,𝔽5) | semidirect |
| 262. #121 | #1043 | semidirect |
| 269. C52 | #1895 | semidirect |
| 386. C5 | #10604494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717435 | 2 |
| #121×C5⋊D5 | 2 |
| C2×#11716875 | 2 |
| #13104777 | 2 |
| #13100253 | 2 |
| #10604494 | 5 |