Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
120 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #15690146 |
| commutator, cosocle, hypocenter | #13095201 | C22×C5 |
| Frattini | C3 | C2×C5×#11759813 |
| Fitting, socle | C2×C3×C5×C132 | D3 |
| LCS | G ▷ #13095201 | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#13095201 | C2 | semidirect |
| 2. C5×#15690146 | C2 | direct (N × H) |
| 4. C5×#13095201 | C22 | semidirect |
| 5. C2×#15690146 | C5 | direct (N × H) |
| 9. C2×#13095201 | C2×C5 | semidirect |
| 10. #15690146 | C2×C5 | direct (N × H) |
| 13. C2×C5×C132 | D9 | semidirect |
| 15. #13095201 | C22×C5 | semidirect |
| 19. C5×C132 | C2×D9 | semidirect |
| 31. C2×C132 | C5×D9 | semidirect |
| 41. C132 | C2×C5×D9 | semidirect |
| 90. C2×C5 | #15690146 | direct (N × H) |
| 94. C5 | C2×#15690146 | direct (N × H) |
| 98. C2 | C5×#15690146 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#13095201 | 2 |
| C5×#15690146 | 2 |
| C2×C5×C13×D39 | 3 |
| C2×#15690146 | 5 |
| C2×C5×D9 | 169 |