Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
495 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 140 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. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 4. C5×(C2×AGL(1,𝔽5))⋊C4 | C2 | semidirect |
| 7. C22×C4×C52 | C4 | semidirect |
| 8. C22×C5×Dic5 | C4 | semidirect |
| 10. C2×C4×C5×D5 | C4 | semidirect |
| 11. C2×C4×C5×D5 | C4 | semidirect |
| 16. #65765 | C5 | direct (N × H) |
| 41. C2×C4⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 44. (C2×AGL(1,𝔽5))⋊C4 | C2×C5 | semidirect |
| 48. C22×C52 | C4⋊C4 | semidirect |
| 54. C2×C5×D5 | C4⋊C4 | semidirect |
| 61. C4×C52 | C22⋊C4 | semidirect |
| 63. C5×Dic5 | C22⋊C4 | semidirect |
| 75. C22×C4×C5 | C4×C5 | semidirect |
| 76. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 77. C22×Dic5 | C4×C5 | semidirect |
| 79. C2×C4×D5 | C4×C5 | semidirect |
| 80. C2×C4×D5 | C4×C5 | semidirect |
| 143. C52 | #380 | semidirect |
| 161. C22×C5 | C5×C4⋊C4 | semidirect |
| 162. C22×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 169. C2×D5 | C5×C4⋊C4 | semidirect |
| 182. C4×C5 | C5×C22⋊C4 | semidirect |
| 183. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 185. Dic5 | C5×C22⋊C4 | semidirect |
| 194. C22×C4 | C5×AGL(1,𝔽5) | semidirect |
| 236. C5 | C5×#380 | semidirect |
| 237. C5 | #65765 | direct (N × H) |
| 249. C22 | C5×C4⋊AGL(1,𝔽5) | semidirect |
| 255. C4 | C5×C22⋊AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×C5×C22⋊AGL(1,𝔽5) | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C5×(C2×AGL(1,𝔽5))⋊C4 | 2 |
| #65765 | 5 |
| C5×#380 | 5 |