Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 291 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×C52×Q8 | C2 | semidirect |
| 3. C2×#87812 | C2 | semidirect |
| 4. #11717262 | C2 | direct (N × H) |
| 5. C2×#87811 | C2 | semidirect |
| 6. C2×#87804 | C2 | semidirect |
| 10. C2×C52×Q8 | C22 | semidirect |
| 19. #87812 | C22 | semidirect |
| 20. #87811 | C22 | semidirect |
| 21. #87804 | C22 | semidirect |
| 43. C22×C5×Q8 | D5 | semidirect |
| 62. C2×C5×Q8 | C2×D5 | semidirect |
| 77. C2×C52 | #137 | semidirect |
| 100. C22×Q8 | C5⋊D5 | semidirect |
| 105. C52 | C2×#137 | semidirect |
| 122. C2×Q8 | C2×C5⋊D5 | semidirect |
| 133. C2×C5 | #4088 | semidirect |
| 155. C5 | C2×#4088 | semidirect |
| 168. C2 | #11717262 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C2×#87900 | 2 |
| C2×#87812 | 2 |
| #11717262 | 2 |
| C2×#87811 | 2 |
| C2×#87804 | 2 |
| C2×#4088 | 5 |