Finite Group DatabasebetaFinite Group DatabasebetaOrder 2400.
290 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 34 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 | D5×C5⋊S4 |
| commutator, cosocle | C2×C52×A4 | C22 |
| Fitting, socle | C23×C52 | C2×D3 |
| hypocenter | C52×A4 | D4 |
| LCS | G ▷ C2×C52×A4 ▷ C52×A4 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5⋊(C5⋊S4) | C2 | semidirect |
| 2. C2×C5×C5⋊S4 | C2 | semidirect |
| 3. C5×A4×Dic5 | C2 | semidirect |
| 13. C22×C5×Dic5 | D3 | semidirect |
| 20. C52×A4 | D4 | semidirect |
| 25. C2×C5⋊S4 | D5 | semidirect |
| 28. A4×Dic5 | D5 | semidirect |
| 59. C22×C52 | D12 | semidirect |
| 69. C5×Dic5 | S4 | semidirect |
| 78. C22×Dic5 | D15 | semidirect |
| 93. C5×A4 | D20 | semidirect |
| 94. C5×A4 | C22⋊D5 | semidirect |
| 145. C52 | C4⋊S4 | semidirect |
| 160. C22×C5 | #1203 | semidirect |
| 161. C22×C5 | D60 | semidirect |
| 182. Dic5 | C5⋊S4 | semidirect |
| 195. A4 | #6038 | semidirect |
| 228. C5 | #91902 | semidirect |
| 229. C5 | C4⋊(C5⋊S4) | semidirect |
| 238. C22 | #10597122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5⋊(C5⋊S4) | 2 |
| C2×C5×C5⋊S4 | 2 |
| C5×A4×Dic5 | 2 |
| #11717096 | 3 |
| #10597122 | 4 |
| C4⋊(C5⋊S4) | 5 |
| #91902 | 5 |