Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
223 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 223 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. #11716745 | C2 | direct (N × H) |
| 69. C2×C52 | #108 | semidirect |
| 101. C52 | C2×#108 | semidirect |
| 136. C2×C5 | #3954 | semidirect |
| 137. C2×C5 | #3996 | semidirect |
| 154. C5 | C2×#3954 | semidirect |
| 155. C5 | C2×#3996 | semidirect |
| 166. C2 | #11716745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C2×C5×#700 | 2 |
| C2×D5×#168 | 2 |
| #11716745 | 2 |
| C2×#3996 | 5 |
| C2×#3954 | 5 |