Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
562 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13099850 | C2 | direct (N × H) |
| 8. C2×#87765 | C4 | semidirect |
| 9. #11716882 | C4 | semidirect |
| 13. C2×C5×#672 | C4 | semidirect |
| 14. #11716583 | C4 | semidirect |
| 30. #87765 | C2×C4 | semidirect |
| 31. C5×#672 | C2×C4 | semidirect |
| 65. C2×#672 | AGL(1,𝔽5) | semidirect |
| 106. #672 | C2×AGL(1,𝔽5) | semidirect |
| 111. C2×C52 | #346 | semidirect |
| 113. C5⋊D5 | #346 | semidirect |
| 155. C52 | C2×#346 | semidirect |
| 192. C2×C5 | #64844 | semidirect |
| 213. C5 | C2×#64844 | semidirect |
| 225. C2 | #13099850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11716882 | 2 |
| C2×C8×#1043 | 2 |
| C2×#11716583 | 2 |
| #13099850 | 2 |
| C2×#64844 | 5 |