Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
205 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 205 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. C23×C5×D5 | C4 | semidirect |
| 9. C52×C22⋊C4 | C4 | semidirect |
| 11. #64864 | C5 | direct (N × H) |
| 26. #4013 | C2×C5 | semidirect |
| 27. #4011 | C2×C5 | semidirect |
| 44. C23×D5 | C4×C5 | semidirect |
| 55. C5×C22⋊C4 | C4×C5 | semidirect |
| 56. C5×C22⋊C4 | AGL(1,𝔽5) | semidirect |
| 91. C52 | AΣL(1,𝔽16) | semidirect |
| 128. C22⋊C4 | C5×AGL(1,𝔽5) | semidirect |
| 154. C5 | C5×AΣL(1,𝔽16) | semidirect |
| 155. C5 | #64864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4028 | 2 |
| C5×#4013 | 2 |
| C5×#4011 | 2 |
| #64864 | 5 |
| C5×AΣL(1,𝔽16) | 5 |