Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
742 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 92 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. #13104866 | C2 | semidirect |
| 4. #13104827 | C2 | semidirect |
| 6. #13100369 | C2 | semidirect |
| 7. #13100332 | C2 | semidirect |
| 25. C52×#104 | C4 | semidirect |
| 26. #11716704 | C4 | semidirect |
| 27. #11716692 | C4 | semidirect |
| 28. #11716672 | C4 | semidirect |
| 59. C52×M16 | C2×C4 | semidirect |
| 60. C42×C52 | C2×C4 | semidirect |
| 62. C4×#1039 | C2×C4 | semidirect |
| 63. #87804 | C2×C4 | semidirect |
| 132. C5×#104 | AGL(1,𝔽5) | semidirect |
| 203. C5×M16 | C2×AGL(1,𝔽5) | semidirect |
| 205. C42×C5 | C2×AGL(1,𝔽5) | semidirect |
| 313. #104 | #1044 | semidirect |
| 317. C52 | #1860 | semidirect |
| 375. M16 | C2×#1044 | semidirect |
| 391. C42 | C2×#1044 | semidirect |
| 444. C5 | #10604004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107775 | 2 |
| #13104932 | 2 |
| #13104866 | 2 |
| #13104827 | 2 |
| #104×C5⋊D5 | 2 |
| #13100369 | 2 |
| #13100332 | 2 |
| #10604004 | 5 |