Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
346 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 74 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. C5×#64683 | C2 | semidirect |
| 9. #10598278 | C5 | direct (N × H) |
| 23. #64683 | C2×C5 | semidirect |
| 117. C52 | #1359 | semidirect |
| 164. C5 | #10598278 | direct (N × H) |
| 165. C5 | C5×#1359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#492 | 2 |
| C5×#64683 | 2 |
| C5×#1359 | 5 |
| #10598278 | 5 |