Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 8. C4⋊#1043 | C4 | semidirect |
| 10. #87856 | C4 | semidirect |
| 12. C42×C52 | C4 | semidirect |
| 14. C4×#1039 | C4 | semidirect |
| 50. C42×C5 | AGL(1,𝔽5) | semidirect |
| 73. C52 | #339 | semidirect |
| 95. C42 | #1043 | semidirect |
| 112. C5 | #64862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717438 | 2 |
| #11717435 | 2 |
| C42×C5⋊D5 | 2 |
| #64862 | 5 |