Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
543 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 113 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×C22⋊#1042 | C2 | semidirect |
| 3. C2×C4⋊#1042 | C2 | semidirect |
| 4. C2×C4×#1042 | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 9. C2×C5×C22⋊D5 | C4 | semidirect |
| 12. C2×C5×D20 | C4 | semidirect |
| 30. C2×#1042 | D4 | semidirect |
| 60. C4×C52 | C22⋊C4 | semidirect |
| 61. C5×Dic5 | C22⋊C4 | semidirect |
| 71. C2×C5×D4 | Dic5 | semidirect |
| 72. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 74. C2×C22⋊D5 | Dic5 | semidirect |
| 79. C2×D20 | Dic5 | semidirect |
| 140. C52 | #390 | semidirect |
| 172. C4×C5 | C22⋊Dic5 | semidirect |
| 173. C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 176. Dic5 | C22⋊Dic5 | semidirect |
| 182. C2×D4 | #1042 | semidirect |
| 226. C5 | #65510 | semidirect |
| 227. C5 | #65780 | semidirect |
| 243. C4 | C22⋊#1042 | semidirect |
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×C22⋊#1042 | 2 |
| C2×C4⋊#1042 | 2 |
| C2×C4×#1042 | 2 |
| #65780 | 5 |
| #65510 | 5 |