Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
319 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11716758 | C2 | direct (N × H) |
| 93. C2×C52 | #101 | semidirect |
| 141. C52 | C2×#101 | semidirect |
| 190. C2×C5 | #3956 | semidirect |
| 191. C2×C5 | #4005 | semidirect |
| 214. C5 | C2×#3956 | semidirect |
| 215. C5 | C2×#4005 | semidirect |
| 228. C2 | #11716758 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C2×#87853 | 2 |
| C2×C5×#704 | 2 |
| #11716758 | 2 |
| C2×#4005 | 5 |
| C2×#3956 | 5 |