Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 90 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×#677 | C2 | semidirect |
| 3. C4×C5×Dic10 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 17. #65137 | C5 | direct (N × H) |
| 29. C5×Dic10 | D4 | semidirect |
| 34. C2×#677 | C2×C5 | semidirect |
| 36. C4×Dic10 | C2×C5 | semidirect |
| 38. C5×C4⋊C8 | D5 | semidirect |
| 39. C5×C4⋊C8 | C2×C5 | semidirect |
| 41. #3953 | C2×C5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 105. Dic10 | C5×D4 | semidirect |
| 112. C4⋊C8 | C5×D5 | semidirect |
| 114. C52 | #460 | semidirect |
| 132. C4×C5 | #677 | semidirect |
| 133. C4×C5 | C5×SD16 | semidirect |
| 175. C5 | #65137 | direct (N × H) |
| 176. C5 | C5×#460 | semidirect |
| 184. C4 | C5×#677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#677 | 2 |
| C5×#4020 | 2 |
| C4×C5×Dic10 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#460 | 5 |
| #65137 | 5 |