Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
187 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 187 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×#3999 | C2 | semidirect |
| 4. C2×C5×D20 | C4 | semidirect |
| 7. C42×C52 | C4 | semidirect |
| 8. #64853 | C5 | direct (N × H) |
| 20. #3999 | C2×C5 | semidirect |
| 34. C2×D20 | C4×C5 | semidirect |
| 39. C42×C5 | C4×C5 | semidirect |
| 40. C42×C5 | AGL(1,𝔽5) | semidirect |
| 66. C52 | #353 | semidirect |
| 90. C42 | C5×AGL(1,𝔽5) | semidirect |
| 110. C5 | C5×#353 | semidirect |
| 111. C5 | #64853 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4020 | 2 |
| C5×#3999 | 2 |
| #64853 | 5 |
| C5×#353 | 5 |