Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
100 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C19×C52⋊C9 | C22 |
| Frattini | C3 | ((C5⋊D5)⋊C3)⋊D19 |
| Fitting, socle | C3×C52×C19 | C2×D3 |
| LCS | G ▷ C19×C52⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C19×(C5⋊D5)⋊C9 | C2 | semidirect |
| 2. C19⋊#90646 | C2 | semidirect |
| 3. C19⋊#90646 | C2 | semidirect |
| 5. C19×C52⋊C9 | C22 | semidirect |
| 13. C19×C5⋊D5 | D9 | semidirect |
| 24. C52×C19 | C2×D9 | semidirect |
| 25. (C5⋊D5)⋊C9 | D19 | semidirect |
| 37. C52⋊C9 | C2×D19 | semidirect |
| 59. C5⋊D5 | D171 | semidirect |
| 72. C52 | C2×D171 | semidirect |
| 75. C19 | #90646⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19×(C5⋊D5)⋊C9 | 2 |
| C19⋊#90646 | 2 |
| #19152888 | 3 |
| #90646⋊C2 | 19 |
| C2×D171 | 25 |