Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
153 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 5. C22×C5×Dic5 | C4 | semidirect |
| 8. C52×C22⋊C4 | C4 | semidirect |
| 11. #64865 | C5 | direct (N × H) |
| 40. C22×Dic5 | C4×C5 | semidirect |
| 48. C5×C22⋊C4 | C4×C5 | semidirect |
| 49. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 80. C52 | #352 | semidirect |
| 109. C22⋊C4 | C5×AGL(1,𝔽5) | semidirect |
| 131. C5 | C5×#352 | semidirect |
| 132. C5 | #64865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4032 | 2 |
| C5×#4013 | 2 |
| C5×#4011 | 2 |
| #64865 | 5 |
| C5×#352 | 5 |