Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C2×#87799 | C2 | semidirect |
| 2. C2×C8×C5⋊D5 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. #11716687 | C2 | semidirect |
| 6. #11716687 | C2 | semidirect |
| 7. #11716670 | C2 | semidirect |
| 37. #6029 | D4 | semidirect |
| 41. C5×C4⋊C8 | D5 | semidirect |
| 51. C2×C5⋊D5 | M16 | semidirect |
| 96. C4⋊C8 | C5⋊D5 | semidirect |
| 100. C52 | #435 | semidirect |
| 148. C5 | #65125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| C2×C8×C5⋊D5 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C52×C4⋊C8 | 2 |
| #11716687 | 2 |
| #11716670 | 2 |
| #65125 | 5 |