Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
301 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 65 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. C22×#1042 | C4 | semidirect |
| 11. C22⋊#1042 | C4 | semidirect |
| 12. C52×C22⋊C4 | C4 | semidirect |
| 13. C5×C22⋊Dic5 | C4 | semidirect |
| 71. C5×C22⋊C4 | Dic5 | semidirect |
| 72. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 77. C22⋊Dic5 | Dic5 | semidirect |
| 123. C52 | #342 | semidirect |
| 175. C22⋊C4 | #1042 | semidirect |
| 212. C5 | #64747 | semidirect |
| 213. C5 | #64866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1042 | 2 |
| C5×D5×C22⋊C4 | 2 |
| #64866 | 5 |
| #64747 | 5 |