Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
255 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 255 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 |
|---|---|---|
| 2. C5×#4013 | C2 | semidirect |
| 3. C5×#4011 | C2 | semidirect |
| 4. C24×C52 | C4 | semidirect |
| 10. C5×C22⋊Dic5 | C4 | semidirect |
| 11. #64934 | C5 | direct (N × H) |
| 26. #4013 | C2×C5 | semidirect |
| 27. #4011 | C2×C5 | semidirect |
| 44. C24×C5 | C4×C5 | semidirect |
| 45. C24×C5 | AGL(1,𝔽5) | semidirect |
| 57. C22⋊Dic5 | C4×C5 | semidirect |
| 93. C52 | AΣL(1,𝔽16) | semidirect |
| 128. C24 | C5×AGL(1,𝔽5) | semidirect |
| 161. C5 | C5×AΣL(1,𝔽16) | semidirect |
| 162. C5 | #64934 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4099 | 2 |
| C5×#4013 | 2 |
| C5×#4011 | 2 |
| #64934 | 5 |
| C5×AΣL(1,𝔽16) | 5 |