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. #11716615 | C2 | direct (N × H) |
| 6. C2×#6029 | C4 | semidirect |
| 18. #6029 | C2×C4 | semidirect |
| 44. C2×C52 | #106 | semidirect |
| 66. C52 | C2×#106 | semidirect |
| 91. C2×C5 | #3940 | semidirect |
| 104. C5 | C2×#3940 | semidirect |
| 112. C2 | #11716615 | 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 |
| #11716615 | 2 |
| C2×#3940 | 5 |