Subgroups — C₅⋊(#15692425⋊C₂) #44570432

Order 32490.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692425	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(D₃₆₁⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#15692425⋊C₂	—	5	1	no	maximal, Hall
4	C₅×C₃₆₁⋊C₃	C₂×C₃	1	1	yes	characteristic
5	D₁₈₀₅	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692425	D₅	1	1	yes	characteristic, complemented, Hall
7	D₃₆₁⋊C₃	—	5	1	no	—
8	C₅×C₃₆₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅⋊AGL(1,𝔽₁₉)	—	19	1	no	maximal
10	C₃₆₁⋊C₃	C₃×D₅	1	1	yes	characteristic
11	C₅×#4296	—	19	1	no	—
12	D₃₆₁	—	5	1	no	Hall
13	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
14	C₃₆₁	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
15	AGL(1,𝔽₁₉)	—	95	1	no	—
16	C₅×C₁₉⋊C₃	—	19	1	no	—
17	D₉₅	—	19	1	no	—
18	#4296	—	19	1	no	—
19	D₁₉⋊C₃	—	95	1	no	—
20	C₅×C₁₉	AGL(1,𝔽₁₉)	1	1	yes	characteristic
21	C₉×D₅	—	361	1	no	Hall
22	C₁₉⋊C₃	—	19	1	no	—
23	C₅×C₉	—	361	1	no	Hall
24	D₁₉	—	95	1	no	—
25	C₃×D₅	—	361	1	no	—
26	C₁₉	C₅⋊AGL(1,𝔽₁₉)	1	1	yes	characteristic
27	C₂×C₉	—	1805	1	no	Hall
28	C₃×C₅	—	361	1	no	—
29	D₅	—	361	1	no	Hall
30	C₉	—	361	1	no	Sylow
31	C₂×C₃	—	1805	1	no	—
32	C₅	#15692425⋊C₂	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	361	1	no	—
34	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₃₆₁	C₂×C₉
Frattini	C₁₉	C₅⋊AGL(1,𝔽₁₉)
socle	C₅×C₁₉	AGL(1,𝔽₁₉)
prime radical	C₅⋊(D₃₆₁⋊C₃)	C₃
cosocle	C₅×C₃₆₁⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₃₆₁
UCS	C₁

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.