Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
520 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 4. #11716675 | C2 | direct (N × H) |
| 12. C2×#6029 | C4 | semidirect |
| 24. #6029 | C2×C4 | semidirect |
| 48. C2×C52 | #106 | semidirect |
| 66. C52 | C2×#106 | semidirect |
| 85. C2×C5 | #3940 | semidirect |
| 99. C5 | C2×#3940 | semidirect |
| 109. C2 | #11716675 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×C4⋊C4 | 2 |
| C2×C4⋊#1039 | 2 |
| C22×#6029 | 2 |
| #11716675 | 2 |
| C2×#3940 | 5 |