Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
543 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×#1042 | C2 | semidirect |
| 4. #11716849 | 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 |
| 14. C22⋊#1042 | C4 | direct (N × H) |
| 26. C2×#1042 | C2×C4 | semidirect |
| 47. C22×C52 | C42 | semidirect |
| 52. C2×C5×D5 | C42 | semidirect |
| 58. C4×C52 | C22⋊C4 | semidirect |
| 60. C5×Dic5 | C22⋊C4 | semidirect |
| 71. C22×C4×C5 | Dic5 | semidirect |
| 72. C22×C4×C5 | AGL(1,𝔽5) | semidirect |
| 74. C22×Dic5 | Dic5 | semidirect |
| 76. C2×C4×D5 | Dic5 | semidirect |
| 77. C2×C4×D5 | Dic5 | semidirect |
| 137. C52 | C4×C22⋊C4 | semidirect |
| 153. C22×C5 | C4×Dic5 | semidirect |
| 154. C22×C5 | C4×AGL(1,𝔽5) | semidirect |
| 160. C2×D5 | C4×Dic5 | semidirect |
| 171. C4×C5 | C22⋊Dic5 | semidirect |
| 172. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 175. Dic5 | C22⋊Dic5 | semidirect |
| 184. C22×C4 | #1042 | semidirect |
| 223. C5 | C4×C22⋊Dic5 | semidirect |
| 224. C5 | C4×C22⋊AGL(1,𝔽5) | semidirect |
| 234. C22 | C4×#1042 | semidirect |
| 240. C4 | C22⋊#1042 | direct (N × H) |
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×C22⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| #11716849 | 2 |
| C4×C22⋊AGL(1,𝔽5) | 5 |
| C4×C22⋊Dic5 | 5 |