Subgroups — C₂²⋊(C₅²⋊#4294) #30685617

Order 17100.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅²×C₁₉	C₃	1	1	yes	maximal, characteristic
2	C₅²⋊#4294	—	4	1	no	maximal, Hall
3	C₂×C₃×C₅²×C₁₉	—	3	1	no	—
4	C₂²×C₅²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×C₁₉	A₄	1	1	yes	characteristic
6	C₂²×C₃×C₅×C₁₉	—	3	2	no	—
7	C₂×C₅²×C₁₉	—	3	1	no	—
8	C₂²⋊(C₅²⋊C₉)	—	19	1	no	maximal, Hall
9	C₂²⋊#4294	—	25	1	no	maximal, Hall
10	C₂×C₃×C₅×C₁₉	—	3	6	no	—
11	C₅²×C₁₉	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₅×C₁₉	—	3	2	no	—
13	C₂²×C₃×C₅²	C₁₉⋊C₃	1	1	yes	characteristic
14	C₃×C₅×C₁₉	—	3	2	no	—
15	C₂²×C₃×C₁₉	C₅²⋊C₃	1	1	yes	characteristic
16	C₅²⋊C₉	—	76	1	no	Hall
17	C₂×C₅×C₁₉	—	3	6	no	—
18	#4294	—	100	1	no	Hall
19	C₂×C₃×C₅²	—	3	1	no	—
20	C₂×C₃×C₁₉	—	3	1	no	—
21	C₂²×C₅²	#4294	1	1	yes	characteristic, complemented, Hall
22	C₅×C₁₉	—	3	2	no	—
23	C₂²×C₁₉	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅²	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
25	C₂²×C₃×C₅	—	3	2	no	—
26	C₃×C₁₉	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic
27	C₂×C₅²	—	3	1	no	—
28	C₂×C₁₉	—	3	1	no	—
29	C₂²⋊C₉	—	475	1	no	Hall
30	C₂×C₃×C₅	—	3	6	no	—
31	C₅²	C₂²⋊#4294	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₅	—	3	2	no	—
33	C₁₉	C₂²⋊(C₅²⋊C₉)	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₅	—	3	2	no	—
35	C₂²×C₃	C₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic
36	C₂×C₅	—	3	6	no	—
37	C₉	—	1900	1	no	Sylow
38	C₂×C₃	—	3	1	no	—
39	C₅	—	3	2	no	—
40	C₂²	C₅²⋊#4294	1	1	yes	characteristic, complemented, Sylow
41	C₃	C₂²⋊(C₁₉⋊(C₅²⋊C₃))	1	1	yes	characteristic
42	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₂²⋊(C₁₉⋊(C₅²⋊C₃))
commutator, hypocenter	C₂²×C₅²×C₁₉	C₉
Fitting, socle, prime radical, cosocle	C₂²×C₃×C₅²×C₁₉	C₃
LCS	G ▷ C₂²×C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂²×C₅²×C₁₉	C₉	semidirect
11. C₅²×C₁₉	C₂²⋊C₉	semidirect
21. C₂²×C₅²	#4294	semidirect
23. C₂²×C₁₉	C₅²⋊C₉	semidirect
31. C₅²	C₂²⋊#4294	semidirect
33. C₁₉	C₂²⋊(C₅²⋊C₉)	semidirect
40. C₂²	C₅²⋊#4294	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅²×C₁₉	3
C₅²⋊#4294	4
C₂²⋊(C₅²⋊C₉)	19
C₂²⋊#4294	25

Subgroups — C22⋊(C52⋊#4294) #30685617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊(C₅²⋊#4294) #30685617