Subgroups — C₅⋊#20266582 #44570472

Order 32490.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692429	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅⋊(C₁₉⋊D₁₉)	C₃	1	1	yes	maximal, characteristic
3	#20266582	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	C₂×C₃	1	1	yes	characteristic
5	C₅⋊(C₁₉⋊D₁₉)	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692429	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₉⋊D₁₉	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅⋊(#4294⋊C₂)	—	19	20	no	maximal
10	C₃×C₁₉²	C₃×D₅	1	1	yes	characteristic
11	C₅×#4294	—	19	20	no	—
12	C₁₉⋊D₁₉	—	5	1	no	Hall
13	C₃×D₉₅	—	19	20	no	—
14	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
15	#4294⋊C₂	—	95	20	no	—
16	C₃×C₅×C₁₉	D₁₉⋊C₃	1	20	yes	—
17	D₉₅	—	19	20	no	—
18	#4294	—	19	20	no	—
19	C₃×D₁₉	—	95	20	no	—
20	C₅×C₁₉	#4294⋊C₂	1	20	yes	complemented
21	C₉×D₅	—	361	1	no	Hall
22	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)	1	20	yes	—
23	C₅×C₉	—	361	1	no	Hall
24	D₁₉	—	95	20	no	—
25	C₃×D₅	—	361	1	no	—
26	C₁₉	C₅⋊(#4294⋊C₂)	1	20	yes	complemented
27	C₂×C₉	—	1805	1	no	Hall
28	C₃×C₅	#14524206	1	1	yes	characteristic
29	D₅	—	361	1	no	Hall
30	C₉	—	361	1	no	Sylow
31	C₂×C₃	—	1805	1	no	—
32	C₅	#20266582	1	1	yes	characteristic, complemented, Sylow
33	C₃	C₅⋊#14524206	1	1	yes	characteristic
34	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊#14524206
commutator, hypocenter	C₅×C₁₉²	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×C₅⋊(C₁₉⋊D₁₉)	C₃
LCS	G ▷ C₅×C₁₉²
UCS	C₁ ◁ C₃

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.