Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
463 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 463 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 3. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 6. C22×C4×C52 | C4 | semidirect |
| 7. C22×C5×Dic5 | C4 | semidirect |
| 9. C2×C4×C5×D5 | C4 | semidirect |
| 12. #65764 | C5 | direct (N × H) |
| 31. (C2×AGL(1,𝔽5))⋊C4 | C2×C5 | semidirect |
| 53. C22×C4×C5 | C4×C5 | semidirect |
| 54. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 55. C22×Dic5 | C4×C5 | semidirect |
| 57. C2×C4×D5 | C4×C5 | semidirect |
| 99. C52 | #381 | semidirect |
| 132. C22×C4 | C5×AGL(1,𝔽5) | semidirect |
| 161. C5 | C5×#381 | semidirect |
| 162. C5 | #65764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65764 | 5 |
| C5×#381 | 5 |