Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
199 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 6. C4×#1042 | C4 | semidirect |
| 7. C2×C52×C8 | C4 | semidirect |
| 8. C2×C5×#168 | C4 | semidirect |
| 39. C2×C5×C8 | Dic5 | semidirect |
| 40. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 44. C2×#168 | Dic5 | semidirect |
| 70. C52 | H(3,ℤ/4) | semidirect |
| 91. C2×C8 | #1042 | semidirect |
| 112. C5 | #64777 | semidirect |
| 113. C5 | #64895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717425 | 2 |
| C2×C5×#676 | 2 |
| #64895 | 5 |
| #64777 | 5 |