Subgroups — #20266582⋊C₅ #44570455

Order 32490.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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