Subgroups — C₅⋊#20266601 #44570554

Order 32490.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692435	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊#14524207	C₃	1	1	yes	maximal, characteristic
3	#20266601	—	5	1	no	maximal, Hall
4	C₅×#11762246	C₂×C₃	1	1	yes	characteristic
5	C₅⋊(C₁₉⋊D₁₉)	C₉	1	1	yes	characteristic, complemented, Hall
6	#15692435	D₅	1	1	yes	characteristic, complemented, Hall
7	#14524207	—	5	1	no	—
8	C₅×C₁₉²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₅⋊AGL(1,𝔽₁₉)	—	19	2	no	maximal
10	#11762246	C₃×D₅	1	1	yes	characteristic
11	C₅×#4296	—	19	2	no	—
12	C₁₉⋊D₁₉	—	5	1	no	Hall
13	C₅⋊(D₁₉⋊C₃)	—	19	2	no	—
14	C₁₉²	C₉×D₅	1	1	yes	characteristic, complemented, Sylow
15	AGL(1,𝔽₁₉)	—	95	2	no	—
16	C₅×C₁₉⋊C₃	—	19	2	no	—
17	D₉₅	—	19	2	no	—
18	D₉₅	—	171	2	no	—
19	#4296	—	19	2	no	—
20	D₁₉⋊C₃	—	95	2	no	—
21	C₅×C₁₉	—	9	2	no	—
22	C₅×C₁₉	AGL(1,𝔽₁₉)	1	2	yes	complemented
23	C₉×D₅	—	361	1	no	Hall
24	C₁₉⋊C₃	—	19	2	no	—
25	C₅×C₉	—	361	1	no	Hall
26	D₁₉	—	855	2	no	—
27	D₁₉	—	95	2	no	—
28	C₃×D₅	—	361	1	no	—
29	C₁₉	—	9	2	no	—
30	C₁₉	C₅⋊AGL(1,𝔽₁₉)	1	2	yes	complemented
31	C₂×C₉	—	1805	1	no	Hall
32	C₃×C₅	—	361	1	no	—
33	D₅	—	361	1	no	Hall
34	C₉	—	361	1	no	Sylow
35	C₂×C₃	—	1805	1	no	—
36	C₅	#20266601	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	361	1	no	—
38	C₂	—	1805	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₉²	C₂×C₉
prime radical	C₅⋊#14524207	C₃
cosocle	C₅×#11762246	C₂×C₃
LCS	G ▷ C₅×C₁₉²
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.