Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
464 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 7. C4×#1044 | C4 | semidirect |
| 8. C42×C52 | C4 | semidirect |
| 9. C4×#1039 | C4 | semidirect |
| 10. C4×#1039 | C4 | semidirect |
| 40. C42×C5 | AGL(1,𝔽5) | semidirect |
| 68. C52 | #376 | semidirect |
| 90. C42 | #1044 | semidirect |
| 107. C5 | #65686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1044 | 2 |
| C42×C5⋊D5 | 2 |
| #11716899 | 2 |
| #65686 | 5 |