Subgroups — C₃⋊(D₂₄₁⋊C₂₅) #49116166

Order 36150.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₄₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₄₁⋊C₂₅	—	3	1	no	maximal, Hall
3	C₅×D₇₂₃	C₅	1	1	yes	maximal, characteristic
4	C₂₄₁⋊C₂₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₂₄₁	C₂×C₅	1	1	yes	characteristic
6	C₅×D₂₄₁	—	3	1	no	—
7	D₇₂₃	C₂₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₄₁	C₅×D₃	1	1	yes	characteristic
9	C₃×C₂₄₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	D₂₄₁	—	3	1	no	Hall
11	C₂₄₁	D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
12	D₃×C₂₅	—	241	1	no	maximal, Hall
13	C₃×C₂₅	—	241	1	no	Hall
14	C₂×C₂₅	—	723	1	no	Hall
15	C₅×D₃	—	241	1	no	—
16	C₂₅	—	241	1	no	Sylow
17	C₃×C₅	D₂₄₁⋊C₅	1	1	yes	characteristic
18	C₂×C₅	—	723	1	no	—
19	D₃	—	241	1	no	Hall
20	C₅	C₃⋊(D₂₄₁⋊C₅)	1	1	yes	characteristic
21	C₃	D₂₄₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	723	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₃⋊(D₂₄₁⋊C₅)
commutator, hypocenter	C₃×C₂₄₁	C₂×C₂₅
Fitting, socle, cosocle	C₃×C₅×C₂₄₁	C₂×C₅
prime radical	C₅×D₇₂₃	C₅
LCS	G ▷ C₃×C₂₄₁
UCS	C₁ ◁ C₅

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.