Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 215 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 |
|---|---|---|
| 3. C4×C52×C8 | C2 | semidirect |
| 4. #11716682 | C2 | semidirect |
| 5. C4×#6029 | C2 | semidirect |
| 13. #87799 | C4 | direct (N × H) |
| 22. C52×C8 | C2×C4 | semidirect |
| 23. #6029 | C2×C4 | semidirect |
| 26. C4×C5×C8 | D5 | semidirect |
| 32. C4×C52 | M16 | semidirect |
| 55. C5×C8 | C4×D5 | semidirect |
| 61. C4×C8 | C5⋊D5 | semidirect |
| 62. C52 | C4×M16 | semidirect |
| 66. C4×C5 | #676 | semidirect |
| 89. C8 | C4×C5⋊D5 | semidirect |
| 90. C5 | C4×#676 | semidirect |
| 96. C4 | #87799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87799 | 2 |
| C42×C5⋊D5 | 2 |
| C4×C52×C8 | 2 |
| #11716682 | 2 |
| C4×#6029 | 2 |
| C4×#676 | 5 |