Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1246 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 245 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 |
|---|---|---|
| 4. #13103963 | C2 | semidirect |
| 5. #13103962 | C2 | semidirect |
| 6. #13103961 | C2 | semidirect |
| 7. C2×#11716771 | C2 | semidirect |
| 17. C5×#4094 | C4 | semidirect |
| 19. #11716935 | C4 | semidirect |
| 46. C5×#681 | C2×C4 | semidirect |
| 47. C2×C5×#168 | C2×C4 | semidirect |
| 48. #87769 | C2×C4 | semidirect |
| 49. #87767 | C2×C4 | semidirect |
| 95. #4094 | AGL(1,𝔽5) | semidirect |
| 153. #681 | C2×AGL(1,𝔽5) | semidirect |
| 154. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 227. C52 | #2912 | semidirect |
| 308. C5 | #10617416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107775 | 2 |
| #13107754 | 2 |
| #13106533 | 2 |
| #13103963 | 2 |
| #13103962 | 2 |
| #13103961 | 2 |
| C2×#11716771 | 2 |
| #10617416 | 5 |