Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
608 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×C5×#681 | C2 | semidirect |
| 3. #11716600 | C2 | direct (N × H) |
| 11. C5×#681 | C22 | semidirect |
| 29. C2×#681 | D5 | semidirect |
| 59. #681 | C2×D5 | semidirect |
| 64. C2×C52 | #100 | semidirect |
| 98. C52 | C2×#100 | semidirect |
| 136. C2×C5 | #3955 | semidirect |
| 153. C5 | C2×#3955 | semidirect |
| 167. C2 | #11716600 | 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×#681 | 2 |
| #11716600 | 2 |
| C2×#3955 | 5 |