Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1174 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 189 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. #13107542 | C2 | semidirect |
| 5. #13104062 | C2 | semidirect |
| 6. #13104061 | C2 | semidirect |
| 7. #13103961 | C2 | semidirect |
| 8. #13103938 | C2 | semidirect |
| 9. #13103909 | C2 | semidirect |
| 20. #11717355 | C22 | semidirect |
| 22. C2×C5×#687 | C4 | semidirect |
| 23. #11717048 | C4 | semidirect |
| 26. C2×#87774 | C4 | semidirect |
| 29. #11716772 | C22 | semidirect |
| 30. #11716771 | C22 | semidirect |
| 31. #11716768 | C22 | semidirect |
| 32. #11716764 | C22 | semidirect |
| 33. #11716762 | C22 | semidirect |
| 45. C2×C5×Dic10 | C2×C4 | semidirect |
| 50. #87872 | C2×C4 | semidirect |
| 67. C5×#687 | C2×C4 | semidirect |
| 68. C5×#687 | C2×C4 | semidirect |
| 69. C2×C5×#168 | C2×C4 | semidirect |
| 70. #87774 | C2×C4 | semidirect |
| 71. #87774 | C2×C4 | semidirect |
| 72. #87767 | C2×C4 | semidirect |
| 134. C2×#687 | AGL(1,𝔽5) | semidirect |
| 193. C2×Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 220. #687 | C2×AGL(1,𝔽5) | semidirect |
| 221. #687 | C2×AGL(1,𝔽5) | semidirect |
| 222. C2×#168 | C2×AGL(1,𝔽5) | semidirect |
| 325. C52 | #2949 | semidirect |
| 445. C5 | #10617428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107767 | 2 |
| #13107542 | 2 |
| C2×#11717048 | 2 |
| #13104783 | 2 |
| #13104062 | 2 |
| #13104061 | 2 |
| #13103961 | 2 |
| #13103938 | 2 |
| #13103909 | 2 |
| #10617428 | 5 |