Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
146 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 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. C52×C4⋊C4 | C2 | semidirect |
| 5. C5×C4⋊Dic5 | C2 | semidirect |
| 6. C5×#683 | C2 | semidirect |
| 7. C4×C5×Dic5 | C2 | semidirect |
| 16. #4044 | C5 | direct (N × H) |
| 30. C5×C4⋊C4 | D5 | semidirect |
| 31. C5×C4⋊C4 | C2×C5 | semidirect |
| 39. C4⋊Dic5 | C2×C5 | semidirect |
| 40. #683 | C2×C5 | semidirect |
| 41. C4×Dic5 | C2×C5 | semidirect |
| 64. C52 | #126 | semidirect |
| 91. C4⋊C4 | C5×D5 | semidirect |
| 115. C5 | #4044 | direct (N × H) |
| 116. C5 | C5×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊C4 | 2 |
| C5×#685 | 2 |
| C5×C4⋊Dic5 | 2 |
| C5×#683 | 2 |
| C4×C5×Dic5 | 2 |
| C5×#126 | 5 |
| #4044 | 5 |