Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. C52×C4⋊C8 | C2 | semidirect |
| 4. #11716687 | C2 | semidirect |
| 5. C4×#6029 | C2 | semidirect |
| 26. #6029 | D4 | semidirect |
| 29. C5×C4⋊C8 | D5 | semidirect |
| 37. C4×C52 | M16 | semidirect |
| 68. C4⋊C8 | C5⋊D5 | semidirect |
| 71. C52 | #436 | semidirect |
| 77. C4×C5 | #676 | semidirect |
| 105. C5 | #65127 | semidirect |
| 112. C4 | #87799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| C52×C4⋊C8 | 2 |
| #11716687 | 2 |
| C4×#6029 | 2 |
| #65127 | 5 |