Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1032 conjugacy classes of subgroups; only the 395 normal subgroups are shown.
This group has 1032 conjugacy classes of subgroups — too many to draw. Only its 395 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. C2×C4×#1039 | C2 | semidirect |
| 4. #11716698 | C2 | semidirect |
| 7. C22×C4×C52 | C4 | semidirect |
| 11. C22⋊#1039 | C4 | direct (N × H) |
| 26. C2×#1039 | C2×C4 | semidirect |
| 34. C22×C52 | C42 | semidirect |
| 40. C4×C52 | C22⋊C4 | semidirect |
| 44. C22×C4×C5 | Dic5 | semidirect |
| 73. C52 | C4×C22⋊C4 | semidirect |
| 77. C22×C5 | C4×Dic5 | semidirect |
| 83. C4×C5 | C22⋊Dic5 | semidirect |
| 88. C22×C4 | #1039 | semidirect |
| 111. C5 | C4×C22⋊Dic5 | semidirect |
| 115. C22 | C4×#1039 | semidirect |
| 122. C4 | C22⋊#1039 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×C4×#1039 | 2 |
| #11716698 | 2 |
| C4×C22⋊Dic5 | 5 |