Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 259 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×C52×C4⋊C4 | C2 | semidirect |
| 3. C22×#6029 | C2 | semidirect |
| 4. #11716676 | C2 | direct (N × H) |
| 10. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 13. C52×C4⋊C4 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 30. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 33. C2×C5×C4⋊C4 | D5 | semidirect |
| 56. C5×C4⋊C4 | C2×D5 | semidirect |
| 60. C2×C52 | #102 | semidirect |
| 82. C2×C4⋊C4 | C5⋊D5 | semidirect |
| 84. C52 | C2×#102 | semidirect |
| 107. C4⋊C4 | C2×C5⋊D5 | semidirect |
| 108. C2×C5 | #3941 | semidirect |
| 128. C5 | C2×#3941 | semidirect |
| 142. C2 | #11716676 | 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×C52×C4⋊C4 | 2 |
| C22×#6029 | 2 |
| #11716676 | 2 |
| C2×#3941 | 5 |