Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
768 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 168 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. C22×#6039 | C2 | semidirect |
| 3. C2×C4×#1039 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C2×#87778 | C2 | semidirect |
| 6. #11717033 | C2 | direct (N × H) |
| 13. C2×#6039 | C22 | semidirect |
| 16. C4×#1039 | C22 | semidirect |
| 17. C5×#685 | C22 | semidirect |
| 18. #87778 | C22 | semidirect |
| 40. C2×#685 | D5 | semidirect |
| 73. #685 | C2×D5 | semidirect |
| 77. C2×C52 | #124 | semidirect |
| 116. C52 | C2×#124 | semidirect |
| 158. C2×C5 | #4031 | semidirect |
| 179. C5 | C2×#4031 | semidirect |
| 193. C2 | #11717033 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C22×#6037 | 2 |
| C2×C4×#1039 | 2 |
| C2×C5×#685 | 2 |
| C2×#87778 | 2 |
| #11717033 | 2 |
| C2×#4031 | 5 |