Finite Group DatabasebetaFinite Group DatabasebetaOrder 800.
192 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 81 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⋊#1042 | C2 | direct (N × H) |
| 7. C2×C4×C52 | C4 | semidirect |
| 8. C2×C5×Dic5 | C4 | semidirect |
| 9. C4×C5×D5 | C4 | semidirect |
| 19. C4×C52 | C2×C4 | semidirect |
| 20. C5×Dic5 | C2×C4 | semidirect |
| 27. C2×C52 | C4⋊C4 | semidirect |
| 29. C5×D5 | C4⋊C4 | semidirect |
| 40. C2×C4×C5 | Dic5 | semidirect |
| 41. C2×C4×C5 | AGL(1,𝔽5) | semidirect |
| 44. C2×Dic5 | Dic5 | semidirect |
| 45. C4×D5 | Dic5 | semidirect |
| 48. C52 | C2×C4⋊C4 | semidirect |
| 63. C4×C5 | C2×Dic5 | semidirect |
| 64. C4×C5 | C2×AGL(1,𝔽5) | semidirect |
| 66. Dic5 | C2×Dic5 | semidirect |
| 75. C2×C5 | C4⋊Dic5 | semidirect |
| 76. C2×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 79. D5 | C4⋊Dic5 | semidirect |
| 88. C2×C4 | #1042 | semidirect |
| 90. C5 | C2×C4⋊Dic5 | semidirect |
| 91. C5 | C2×C4⋊AGL(1,𝔽5) | semidirect |
| 99. C4 | C2×#1042 | semidirect |
| 103. C2 | C4⋊#1042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1042 | 2 |
| C2×C4×C5×D5 | 2 |
| C4⋊#1042 | 2 |
| C2×C4⋊AGL(1,𝔽5) | 5 |
| C2×C4⋊Dic5 | 5 |