Subgroups — C₅⋊#20266588 #44570480

Order 32490.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15692430	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₂₈₅	—	3	1	no	maximal
3	#20266588	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₉²	D₃	1	1	yes	characteristic
5	C₁₉×D₉₅	—	9	1	no	Hall
6	#15692430	D₅	1	1	yes	characteristic, complemented, Hall
7	C₁₉×D₅₇	—	15	1	no	—
8	C₅×C₁₉²	D₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₉²	D₁₅	1	1	yes	characteristic
10	C₅×#4294	—	38	1	no	—
11	C₁₉×D₁₉	—	45	1	no	Hall
12	D₂₈₅	—	3	1	no	—
13	C₁₉×D₁₅	—	57	1	no	—
14	C₁₉²	D₄₅	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₅×C₁₉	—	2	1	no	—
16	C₃×C₅×C₁₉	—	3	1	no	—
17	C₃×C₅×C₁₉	—	3	1	no	—
18	C₃×C₅×C₁₉	—	6	2	no	—
19	D₉₅	—	9	1	no	—
20	D₅×C₁₉	—	171	1	no	—
21	#4294	—	38	1	no	—
22	D₅₇	—	15	1	no	—
23	D₃×C₁₉	—	285	1	no	—
24	C₅×C₁₉	—	2	1	no	—
25	C₅×C₁₉	—	3	1	no	—
26	C₅×C₁₉	—	3	1	no	—
27	C₅×C₁₉	—	6	2	no	—
28	D₄₅	—	361	1	no	maximal, Hall
29	C₃×C₁₉	—	2	1	no	—
30	C₃×C₁₉	—	3	1	no	—
31	C₃×C₁₉	—	3	1	no	—
32	C₃×C₁₉	—	6	2	no	—
33	C₅×C₉	—	361	1	no	Hall
34	C₂×C₁₉	—	855	1	no	—
35	D₁₉	—	45	1	no	—
36	D₁₅	—	57	1	no	—
37	C₁₉	—	2	1	no	—
38	C₁₉	—	3	1	no	—
39	C₁₉	—	3	1	no	—
40	C₁₉	—	6	2	no	—
41	D₉	—	1805	1	no	Hall
42	C₃×C₅	#14524212	1	1	yes	characteristic
43	D₅	—	171	1	no	Hall
44	C₉	—	361	1	no	Sylow
45	D₃	—	285	1	no	—
46	C₅	#20266588	1	1	yes	characteristic, complemented, Sylow
47	C₃	C₅⋊#14524212	1	1	yes	characteristic
48	C₂	—	855	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₅×#15692430	C₂
Frattini	C₃	C₅⋊#14524212
Fitting, socle	C₃×C₅×C₁₉²	D₃
LCS	G ▷ C₅×#15692430
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.