Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
936 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 379 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 |
| 36. C22×C52 | C4⋊C4 | semidirect |
| 43. C4×C52 | C22⋊C4 | semidirect |
| 47. C22×C4×C5 | Dic5 | semidirect |
| 78. C52 | #380 | semidirect |
| 83. C22×C5 | C4⋊Dic5 | semidirect |
| 90. C4×C5 | C22⋊Dic5 | semidirect |
| 95. C22×C4 | #1039 | semidirect |
| 120. C5 | #65501 | semidirect |
| 125. C22 | C4⋊#1039 | semidirect |
| 133. C4 | C22⋊#1039 | semidirect |
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 |
| #65501 | 5 |