Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
762 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C5 | C23×A4 |
| commutator, cosocle | C2×Q8 | C23×C3×C5 |
| Frattini | C22 | C23×C5×A4 |
| Fitting | C5×#3499 | C3 |
| hypercenter | C5×#127 | A4 |
| hypocenter | Q8 | C2×C3×C5×D4 |
| LCS | G ▷ C2×Q8 ▷ Q8 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×2−1+4⋊C3 | C2 | semidirect |
| 2. C5×D4×SL(2,𝔽3) | C2 | semidirect |
| 3. C4×C5×#41⋊C3 | C2 | semidirect |
| 4. C5×#3499 | C3 | semidirect |
| 10. #3499⋊C3 | C5 | direct (N × H) |
| 11. C2×C5×2−1+4 | C2×C3 | semidirect |
| 12. C5×D4×Q8 | C2×C3 | semidirect |
| 17. C4×C5×#41 | C2×C3 | semidirect |
| 20. C5×#41⋊C3 | D4 | semidirect |
| 24. C2×2−1+4⋊C3 | C2×C5 | semidirect |
| 25. D4×SL(2,𝔽3) | C2×C5 | semidirect |
| 26. C4×#41⋊C3 | C2×C5 | semidirect |
| 48. #3499 | C3×C5 | semidirect |
| 65. C5×#41 | C3×D4 | semidirect |
| 89. C2×2−1+4 | C2×C3×C5 | semidirect |
| 90. D4×Q8 | C2×C3×C5 | semidirect |
| 95. C4×#41 | C2×C3×C5 | semidirect |
| 103. #41⋊C3 | C5×D4 | semidirect |
| 170. C4×C5 | 2−1+4⋊C3 | semidirect |
| 176. #41 | C3×C5×D4 | semidirect |
| 236. C5 | #3499⋊C3 | direct (N × H) |
| 247. C4 | C5×2−1+4⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4⋊C3 | 2 |
| C5×D4×SL(2,𝔽3) | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3499 | 3 |
| C3×C5×#127 | 4 |
| #3499⋊C3 | 5 |