Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
444 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D5⋊AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C3×C52 | C22×C4 |
| prime radical | #11925429 | C2 |
| cosocle | C2×C3×C5⋊D5 | C23 |
| hypocenter | C3×C52 | C4×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10597182 | C2 | semidirect |
| 2. C2×D3×#1044 | C2 | semidirect |
| 4. #11925360 | C2 | semidirect |
| 5. #11925349 | C2 | semidirect |
| 6. (C2×D3)⋊#1043 | C2 | semidirect |
| 7. C3×#87832 | C2 | semidirect |
| 17. #10597122 | C4 | semidirect |
| 18. C5×#1203 | C4 | semidirect |
| 25. #87832 | D3 | semidirect |
| 28. C2×C3⋊(C5⋊D5) | C2×C4 | semidirect |
| 29. C2×C5×D15 | C2×C4 | semidirect |
| 30. C2×C52×D3 | C2×C4 | semidirect |
| 36. C3⋊#1044 | D4 | semidirect |
| 40. C3×C5×Dic5 | C2×C4 | semidirect |
| 82. #1203 | AGL(1,𝔽5) | semidirect |
| 95. C5×Dic5 | C4×D3 | semidirect |
| 105. C3×C52 | C4×D4 | semidirect |
| 108. C2×D15 | C2×AGL(1,𝔽5) | semidirect |
| 111. C2×C5×D3 | C2×AGL(1,𝔽5) | semidirect |
| 127. C3×Dic5 | C2×AGL(1,𝔽5) | semidirect |
| 170. C52 | #893 | semidirect |
| 203. Dic5 | D3×AGL(1,𝔽5) | semidirect |
| 212. C3×C5 | D4×AGL(1,𝔽5) | semidirect |
| 220. C2×D3 | D5⋊AGL(1,𝔽5) | semidirect |
| 256. C5 | #91921 | semidirect |
| 270. C3 | #11717377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597182 | 2 |
| C2×D3×#1044 | 2 |
| #11925429 | 2 |
| #11925360 | 2 |
| #11925349 | 2 |
| (C2×D3)⋊#1043 | 2 |
| C3×#87832 | 2 |
| #11717377 | 3 |
| #91921 | 5 |