Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 2. C22×C5×Dic10 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. C2×#87776 | C2 | semidirect |
| 5. #11716951 | C2 | direct (N × H) |
| 6. C2×#87774 | C2 | semidirect |
| 18. C2×C5×Dic10 | C22 | semidirect |
| 19. C5×#681 | C22 | semidirect |
| 21. #87776 | C22 | semidirect |
| 22. #87774 | C22 | semidirect |
| 48. C22×Dic10 | D5 | semidirect |
| 53. C2×#681 | D5 | semidirect |
| 97. C2×Dic10 | C2×D5 | semidirect |
| 102. #681 | C2×D5 | semidirect |
| 108. C2×C52 | #137 | semidirect |
| 168. C52 | C2×#137 | semidirect |
| 219. C2×C5 | #4055 | semidirect |
| 220. C2×C5 | #4088 | semidirect |
| 246. C5 | C2×#4055 | semidirect |
| 247. C5 | C2×#4088 | semidirect |
| 260. C2 | #11716951 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C22×C5×Dic10 | 2 |
| C2×C5×#681 | 2 |
| C2×#87776 | 2 |
| #11716951 | 2 |
| C2×#87774 | 2 |
| C2×#4088 | 5 |
| C2×#4055 | 5 |