Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
544 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 8. #11716986 | C2 | direct (N × H) |
| 101. C2×C52 | #125 | semidirect |
| 150. C52 | C2×#125 | semidirect |
| 198. C2×C5 | #4016 | semidirect |
| 199. C2×C5 | #4035 | semidirect |
| 222. C5 | C2×#4016 | semidirect |
| 223. C5 | C2×#4035 | semidirect |
| 235. C2 | #11716986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87806 | 2 |
| C2×C5×#683 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×#87781 | 2 |
| C2×#87780 | 2 |
| #11716986 | 2 |
| C2×#4035 | 5 |
| C2×#4016 | 5 |