Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 100 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⋊#1043 | C4 | semidirect |
| 7. C2×C52×C8 | C4 | semidirect |
| 8. C2×#6029 | C4 | semidirect |
| 36. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 57. C52 | #340 | semidirect |
| 71. C2×C8 | #1043 | semidirect |
| 89. C5 | #64893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1043 | 2 |
| C2×C8×C5⋊D5 | 2 |
| #64893 | 5 |