Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
314 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 132 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. C4⋊#6029 | C2 | semidirect |
| 4. C5×C4⋊#168 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 26. C4×C5×D5 | C8 | semidirect |
| 41. C4⋊#168 | D5 | direct (N × H) |
| 47. C4×C52 | C2×C8 | semidirect |
| 52. C5×Dic5 | C2×C8 | semidirect |
| 79. C5×D5 | C4⋊C8 | semidirect |
| 102. C4×D5 | #168 | semidirect |
| 115. C52 | C2×C4⋊C8 | semidirect |
| 134. C4×C5 | C8×D5 | semidirect |
| 135. C4×C5 | C2×#168 | semidirect |
| 141. Dic5 | C2×#168 | semidirect |
| 163. D5 | C4⋊#168 | direct (N × H) |
| 178. C5 | D5×C4⋊C8 | semidirect |
| 179. C5 | C2×C4⋊#168 | semidirect |
| 188. C4 | D5×#168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×D5 | 2 |
| C2×D5×#168 | 2 |
| C4⋊#6029 | 2 |
| C5×C4⋊#168 | 2 |
| #11716612 | 2 |
| C2×C4⋊#168 | 5 |
| D5×C4⋊C8 | 5 |