Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
166 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C5 | #393⋊C3 |
| commutator, cosocle, hypocenter | #543 | C2×C3×C5 |
| Frattini | C24 | C2×C5×A4 |
| Fitting | C5×#2032 | C3 |
| hypercenter | C22×C5 | #120⋊C3 |
| LCS | G ▷ #543 | |
| UCS | C1 ◁ C2×C5 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#543⋊C3 | C2 | semidirect |
| 2. C5×#2032 | C3 | semidirect |
| 4. #2032⋊C3 | C5 | direct (N × H) |
| 5. C5×#543 | C2×C3 | semidirect |
| 12. #543⋊C3 | C2×C5 | semidirect |
| 18. #2032 | C3×C5 | semidirect |
| 25. C24×C5 | SL(2,𝔽3) | semidirect |
| 32. C22×C4×C5 | SL(2,𝔽3) | semidirect |
| 38. #543 | C2×C3×C5 | semidirect |
| 87. C24 | C5×SL(2,𝔽3) | semidirect |
| 94. C22×C4 | C5×SL(2,𝔽3) | semidirect |
| 127. C5 | #2032⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#543⋊C3 | 2 |
| C5×#2032 | 3 |
| C5×D4×A4 | 4 |
| #2032⋊C3 | 5 |