Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
319 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 4. C5×#4009 | C2 | semidirect |
| 5. C2×C52×Q8 | C4 | semidirect |
| 8. C5×Q8×D5 | C4 | semidirect |
| 13. C2×C5×Dic10 | C4 | semidirect |
| 20. #65782 | C5 | direct (N × H) |
| 47. #4009 | C2×C5 | semidirect |
| 67. C2×C5×Q8 | C4×C5 | semidirect |
| 68. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 73. Q8×D5 | C4×C5 | semidirect |
| 78. C2×Dic10 | C4×C5 | semidirect |
| 142. C52 | #419 | semidirect |
| 175. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 214. C5 | C5×#419 | semidirect |
| 215. C5 | #65782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C5×#4130 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4009 | 2 |
| #65782 | 5 |
| C5×#419 | 5 |