Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1320 conjugacy classes of subgroups; only the 651 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 651 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. #11716698 | C2 | direct (N × H) |
| 6. C22×C4×C52 | C4 | semidirect |
| 10. C22×#1039 | C4 | semidirect |
| 21. C2×C4×C52 | C2×C4 | semidirect |
| 25. C2×#1039 | C2×C4 | semidirect |
| 43. C22×C4×C5 | Dic5 | semidirect |
| 50. C2×C52 | #95 | semidirect |
| 64. C2×C4×C5 | C2×Dic5 | semidirect |
| 72. C52 | C2×#95 | semidirect |
| 91. C22×C4 | #1039 | semidirect |
| 93. C2×C5 | #3963 | semidirect |
| 111. C2×C4 | C2×#1039 | semidirect |
| 112. C5 | C2×#3963 | semidirect |
| 125. C2 | #11716698 | 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 |
| C23×#1039 | 2 |
| #11716698 | 2 |
| C2×#3963 | 5 |