Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 262 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 |
|---|---|---|
| 1. C2×C5×Dic20 | C2 | semidirect |
| 4. C4×C5×Dic10 | C2 | semidirect |
| 5. C52×C4⋊C8 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 22. #65134 | C5 | direct (N × H) |
| 42. C2×Dic20 | C2×C5 | semidirect |
| 45. C4×Dic10 | C2×C5 | semidirect |
| 47. C5×C4⋊C8 | D5 | semidirect |
| 48. C5×C4⋊C8 | C2×C5 | semidirect |
| 52. #3948 | C2×C5 | semidirect |
| 137. C4⋊C8 | C5×D5 | semidirect |
| 140. C52 | #464 | semidirect |
| 208. C5 | #65134 | direct (N × H) |
| 209. C5 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Dic20 | 2 |
| C2×C5×#677 | 2 |
| C5×#4021 | 2 |
| C4×C5×Dic10 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3948 | 2 |
| C5×#464 | 5 |
| #65134 | 5 |