Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
142 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 6. #11716579 | C4 | semidirect |
| 75. C52 | #1398 | semidirect |
| 109. C5 | #10598010 | semidirect |
| 110. C5 | #10598537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13100161 | 2 |
| C5×#64681 | 2 |
| #10598537 | 5 |
| #10598010 | 5 |