Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
431 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 431 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 2. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C2×C5×D5⋊C8 | C2 | semidirect |
| 4. C5×#4007 | C2 | direct (N × H) |
| 7. C2×C52×D4 | C4 | semidirect |
| 11. C5×D4×D5 | C4 | semidirect |
| 13. C2×C5×D20 | C4 | semidirect |
| 17. C5×C4⋊AGL(1,𝔽5) | C22 | semidirect |
| 19. C5×D5⋊C8 | C22 | semidirect |
| 20. C2×#4007 | C5 | direct (N × H) |
| 32. C52×D4 | C2×C4 | semidirect |
| 38. C5×D20 | C2×C4 | semidirect |
| 46. C2×C4⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 47. C2×D5⋊C8 | C2×C5 | semidirect |
| 50. #4007 | C2×C5 | direct (N × H) |
| 79. C2×C5×D4 | C4×C5 | semidirect |
| 80. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 86. D4×D5 | C4×C5 | semidirect |
| 88. C2×D20 | C4×C5 | semidirect |
| 92. C4⋊AGL(1,𝔽5) | C22×C5 | semidirect |
| 94. D5⋊C8 | C22×C5 | semidirect |
| 102. C2×C52 | #102 | semidirect |
| 105. C5×D5 | #102 | semidirect |
| 133. C5×D4 | C2×C4×C5 | semidirect |
| 134. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 149. D20 | C2×C4×C5 | semidirect |
| 160. C52 | C2×#102 | semidirect |
| 207. C2×D4 | C5×AGL(1,𝔽5) | semidirect |
| 224. C2×C5 | C5×#102 | semidirect |
| 225. C2×C5 | #4007 | direct (N × H) |
| 229. D5 | C5×#102 | semidirect |
| 244. D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 255. C5 | C2×C5×#102 | semidirect |
| 256. C5 | C2×#4007 | direct (N × H) |
| 279. C2 | C5×#4007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×D5⋊C8 | 2 |
| C5×#4007 | 2 |
| C2×#4007 | 5 |
| C2×C5×#102 | 5 |