Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 136 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. #11716617 | C2 | direct (N × H) |
| 6. C2×#6029 | C4 | semidirect |
| 18. #6029 | C2×C4 | semidirect |
| 45. C2×C52 | #107 | semidirect |
| 68. C52 | C2×#107 | semidirect |
| 95. C2×C5 | #3939 | semidirect |
| 108. C5 | C2×#3939 | semidirect |
| 117. C2 | #11716617 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6029 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| #11716617 | 2 |
| C2×#3939 | 5 |