Finite Group DatabasebetaFinite Group Databasebeta← C22×(C2×AGL(1,𝔽5))⋊D5 #13107639
Order 1600.
1415 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1415 conjugacy classes of subgroups — too many to draw. Only its 290 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. C23×#1042 | C2 | semidirect |
| 3. C23×C5×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×(C2×AGL(1,𝔽5))⋊D5 | C2 | direct (N × H) |
| 5. C23×C5⋊D5 | C4 | semidirect |
| 6. C23×C5×D5 | C4 | semidirect |
| 10. C22×D52 | C4 | semidirect |
| 13. C22×#1042 | C22 | semidirect |
| 15. C22×C5×AGL(1,𝔽5) | C22 | semidirect |
| 16. (C2×AGL(1,𝔽5))⋊D5 | C22 | direct (N × H) |
| 21. C22×C5⋊D5 | C2×C4 | semidirect |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 31. C2×D52 | C2×C4 | semidirect |
| 34. C2×#1042 | C23 | semidirect |
| 36. C2×C5×AGL(1,𝔽5) | C23 | semidirect |
| 40. C23×AGL(1,𝔽5) | D5 | semidirect |
| 45. C22×C52 | C22⋊C4 | semidirect |
| 48. C2×C5⋊D5 | C22×C4 | semidirect |
| 50. C2×C5×D5 | C22⋊C4 | semidirect |
| 52. C2×C5×D5 | C22×C4 | semidirect |
| 74. C23×D5 | AGL(1,𝔽5) | semidirect |
| 79. C22×AGL(1,𝔽5) | C2×D5 | semidirect |
| 87. C2×C52 | C2×C22⋊C4 | semidirect |
| 91. C5×D5 | C2×C22⋊C4 | semidirect |
| 123. C22×D5 | C2×AGL(1,𝔽5) | semidirect |
| 128. C2×AGL(1,𝔽5) | C22×D5 | semidirect |
| 137. C52 | C22×C22⋊C4 | semidirect |
| 147. C22×C5 | #685 | semidirect |
| 148. C22×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 164. C2×D5 | #685 | semidirect |
| 168. C2×D5 | C22×AGL(1,𝔽5) | semidirect |
| 192. C2×C5 | C2×#685 | semidirect |
| 193. C2×C5 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 200. D5 | C2×#685 | semidirect |
| 222. C5 | C22×#685 | semidirect |
| 223. C5 | C22×C22⋊AGL(1,𝔽5) | semidirect |
| 236. C22 | (C2×AGL(1,𝔽5))⋊D5 | direct (N × H) |
| 245. C2 | C2×(C2×AGL(1,𝔽5))⋊D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C23×#1042 | 2 |
| C23×C5×AGL(1,𝔽5) | 2 |
| C2×(C2×AGL(1,𝔽5))⋊D5 | 2 |
| C22×C22⋊AGL(1,𝔽5) | 5 |
| C22×#685 | 5 |