Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
1040 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×C5⋊D5 |
| commutator, socle, cosocle | C22×C3×C52 | C23 |
| Fitting | C23×C3×C52 | C22 |
| hypercenter | C23 | D3×C5⋊D5 |
| hypocenter | C3×C52 | #120 |
| LCS | G ▷ C22×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C3×C5⋊D5 | C2 | semidirect |
| 2. C2×C52×#67 | C2 | semidirect |
| 3. C2×#10597114 | C2 | semidirect |
| 4. #11925254 | C2 | semidirect |
| 5. #11925118 | C2 | semidirect |
| 8. C22×C52×D3 | C22 | semidirect |
| 12. C2×C3⋊#1039 | C22 | semidirect |
| 14. C2×C52×Dic3 | C22 | semidirect |
| 17. C23×C5⋊D5 | D3 | semidirect |
| 23. C22×C3×C52 | D4 | semidirect |
| 30. C2×C3×C5⋊D5 | D4 | semidirect |
| 34. C2×C5×#67 | D5 | semidirect |
| 54. C22×C5×D3 | C2×D5 | semidirect |
| 60. C2×C5×Dic3 | C2×D5 | semidirect |
| 65. C22×C52 | #67 | semidirect |
| 70. C2×C5⋊D5 | #67 | semidirect |
| 79. C3×C52 | #120 | semidirect |
| 81. C22×C3×C5 | C22⋊D5 | semidirect |
| 98. C2×#67 | C5⋊D5 | semidirect |
| 116. C52 | #953 | semidirect |
| 121. C22×D3 | C2×C5⋊D5 | semidirect |
| 125. C2×Dic3 | C2×C5⋊D5 | semidirect |
| 129. C22×C5 | #1201 | semidirect |
| 142. C3×C5 | #4083 | semidirect |
| 148. C22×C3 | C22⋊(C5⋊D5) | semidirect |
| 173. C5 | #91563 | semidirect |
| 181. C22 | #10597114 | semidirect |
| 185. C3 | #11717257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C5⋊D5 | 2 |
| C2×C52×#67 | 2 |
| C2×#10597114 | 2 |
| #11925254 | 2 |
| #11925118 | 2 |
| #11717257 | 3 |
| #91563 | 5 |