Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1320 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 675 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. #11717246 | C2 | direct (N × H) |
| 4. C2×C4⋊#1039 | C2 | semidirect |
| 5. C2×C4×#1039 | C2 | semidirect |
| 7. C22×C4×C52 | C4 | semidirect |
| 13. C4⋊#1039 | C22 | semidirect |
| 14. C4×#1039 | C22 | semidirect |
| 22. C2×C4×C52 | C2×C4 | semidirect |
| 42. C22×C4×C5 | Dic5 | semidirect |
| 52. C2×C52 | #117 | semidirect |
| 61. C2×C4×C5 | C2×Dic5 | semidirect |
| 71. C52 | C2×#117 | semidirect |
| 83. C22×C4 | #1039 | semidirect |
| 91. C2×C5 | #4072 | semidirect |
| 102. C2×C4 | C2×#1039 | semidirect |
| 105. C5 | C2×#4072 | semidirect |
| 116. C2 | #11717246 | 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 |
| #11717246 | 2 |
| C2×C4⋊#1039 | 2 |
| C2×C4×#1039 | 2 |
| C2×#4072 | 5 |