Finite Group DatabasebetaFinite Group DatabasebetaOrder 1200.
110 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 38 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 | AGL(1,𝔽5)×D15 |
| commutator, Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical, cosocle | C2×C3×C5×D5 | C22 |
| hypocenter | C3×C52 | C4⋊C4 |
| 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 |
|---|---|---|
| 8. C3⋊#1039 | C4 | semidirect |
| 9. C5×Dic15 | C4 | semidirect |
| 31. C3×C52 | C4⋊C4 | semidirect |
| 41. Dic15 | AGL(1,𝔽5) | semidirect |
| 60. C52 | Dic3⋊C4 | semidirect |
| 77. C3×C5 | #683 | semidirect |
| 78. C3×C5 | C4⋊AGL(1,𝔽5) | semidirect |
| 98. C5 | #6712 | semidirect |
| 99. C5 | Dic3⋊AGL(1,𝔽5) | semidirect |
| 105. C3 | #87825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#1042 | 2 |
| C2×C3×C5×AGL(1,𝔽5) | 2 |
| D5×Dic15 | 2 |
| #87825 | 3 |
| Dic3⋊AGL(1,𝔽5) | 5 |
| #6712 | 5 |