Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
842 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 13. #11716897 | C4 | semidirect |
| 14. C4⋊#6034 | C4 | semidirect |
| 16. C5×C4⋊#168 | C4 | semidirect |
| 17. #11716613 | C4 | semidirect |
| 84. C4⋊#168 | AGL(1,𝔽5) | semidirect |
| 94. C4×C52 | #97 | semidirect |
| 98. #1039 | #97 | semidirect |
| 201. C52 | #1767 | semidirect |
| 221. C4×C5 | #3992 | semidirect |
| 285. C5 | #10604028 | semidirect |
| 298. C4 | #11716763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104816 | 2 |
| C42×#1043 | 2 |
| C2×#11716763 | 2 |
| #13100510 | 2 |
| #13099895 | 2 |
| #10604028 | 5 |