Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 52 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×#4004 | C2 | semidirect |
| 8. #64925 | C5 | direct (N × H) |
| 21. #4004 | C2×C5 | semidirect |
| 70. C52 | #331 | semidirect |
| 117. C5 | C5×#331 | semidirect |
| 118. C5 | #64925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4086 | 2 |
| C5×#4004 | 2 |
| #64925 | 5 |
| C5×#331 | 5 |