Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 160 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×C4×#1039 | C2 | semidirect |
| 3. C2×C5×#683 | C2 | semidirect |
| 4. C2×#87780 | C2 | semidirect |
| 5. C2×#87780 | C2 | semidirect |
| 8. #11716980 | C2 | direct (N × H) |
| 16. C4×#1039 | C22 | semidirect |
| 18. C5×#683 | C22 | semidirect |
| 19. #87780 | C22 | semidirect |
| 20. #87780 | C22 | semidirect |
| 53. C2×#683 | D5 | semidirect |
| 101. #683 | C2×D5 | semidirect |
| 106. C2×C52 | #126 | semidirect |
| 160. C52 | C2×#126 | semidirect |
| 215. C2×C5 | #4025 | semidirect |
| 216. C2×C5 | #4044 | semidirect |
| 242. C5 | C2×#4025 | semidirect |
| 243. C5 | C2×#4044 | semidirect |
| 259. C2 | #11716980 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| #11716980 | 2 |
| C2×#4044 | 5 |
| C2×#4025 | 5 |