Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
242 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 47 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. C22×#1043 | C2 | semidirect |
| 2. C2×D5⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C22⋊#1044 | C2 | semidirect |
| 5. #87832 | C2 | semidirect |
| 6. #87831 | C2 | semidirect |
| 7. #87830 | C2 | semidirect |
| 16. C5×C22⋊D5 | C4 | semidirect |
| 17. #6038 | C4 | semidirect |
| 20. C22×C52 | C2×C4 | semidirect |
| 23. C2×C5⋊D5 | C2×C4 | semidirect |
| 25. C2×C5×D5 | C2×C4 | semidirect |
| 31. #1043 | D4 | semidirect |
| 32. C5×Dic5 | C2×C4 | semidirect |
| 61. C22⋊D5 | AGL(1,𝔽5) | semidirect |
| 65. C52 | C4×D4 | semidirect |
| 68. C22×C5 | C2×AGL(1,𝔽5) | semidirect |
| 79. C2×D5 | C2×AGL(1,𝔽5) | semidirect |
| 87. Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 119. C5 | D4×AGL(1,𝔽5) | semidirect |
| 127. C22 | D5⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1043 | 2 |
| C2×D5⋊AGL(1,𝔽5) | 2 |
| #87886 | 2 |
| C22⋊#1044 | 2 |
| #87832 | 2 |
| #87831 | 2 |
| #87830 | 2 |
| D4×AGL(1,𝔽5) | 5 |