Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
3138 conjugacy classes of subgroups; only the 339 normal subgroups are shown.
This group has 3138 conjugacy classes of subgroups — too many to draw. Only its 339 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. C22×C4×#1044 | C2 | semidirect |
| 3. C22×C4⋊#1043 | C2 | semidirect |
| 4. C22×#87831 | C2 | semidirect |
| 5. #13103996 | C2 | direct (N × H) |
| 10. C22×C5×D20 | C4 | semidirect |
| 11. C22×#6037 | C4 | semidirect |
| 14. C2×#87877 | C4 | semidirect |
| 17. C2×C4×#1044 | C22 | semidirect |
| 19. C2×C4⋊#1043 | C22 | semidirect |
| 21. C2×#87831 | C22 | semidirect |
| 33. C22×#1044 | D4 | semidirect |
| 45. C2×C5×D20 | C2×C4 | semidirect |
| 47. C2×#6037 | C2×C4 | semidirect |
| 82. C2×#1044 | C2×D4 | semidirect |
| 86. C2×C4×C52 | C22⋊C4 | semidirect |
| 88. C2×#1039 | C22⋊C4 | semidirect |
| 90. C4×C5⋊D5 | C22⋊C4 | semidirect |
| 105. C22×D20 | AGL(1,𝔽5) | semidirect |
| 138. C4×C52 | C2×C22⋊C4 | semidirect |
| 139. #1039 | C2×C22⋊C4 | semidirect |
| 172. C2×D20 | C2×AGL(1,𝔽5) | semidirect |
| 190. C2×C52 | #390 | semidirect |
| 193. C5⋊D5 | #390 | semidirect |
| 240. C2×C4×C5 | C22⋊AGL(1,𝔽5) | semidirect |
| 270. C52 | C2×#390 | semidirect |
| 309. C4×C5 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 347. C2×C5 | #65780 | semidirect |
| 392. C2×C4 | #87831 | semidirect |
| 395. C5 | C2×#65780 | semidirect |
| 418. C4 | C2×#87831 | semidirect |
| 424. C2 | #13103996 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#87877 | 2 |
| C22×C4×#1044 | 2 |
| C22×C4⋊#1043 | 2 |
| C22×#87831 | 2 |
| #13103996 | 2 |
| C2×#65780 | 5 |