Subgroups — C₂²×C₅²⋊#4294 #30685613

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊#4294	C₂	direct (N × H)
3. C₅²⋊#4294	C₂²	direct (N × H)
5. C₂²×C₅²×C₁₉	C₉	semidirect
8. C₂×C₅²×C₁₉	C₂×C₉	semidirect
12. C₅²×C₁₉	C₂²×C₉	semidirect
24. C₂²×C₅²	#4294	semidirect
26. C₂²×C₁₉	C₅²⋊C₉	semidirect
30. C₂×C₅²	C₂×#4294	semidirect
31. C₂×C₁₉	C₂×C₅²⋊C₉	semidirect
34. C₅²	C₂²×#4294	semidirect
36. C₁₉	C₂²×C₅²⋊C₉	semidirect
44. C₂²	C₅²⋊#4294	direct (N × H)
46. C₂	C₂×C₅²⋊#4294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅²⋊#4294	2
C₂²×C₃×C₅²×C₁₉	3
C₂²×C₅²⋊C₉	19
C₂²×#4294	25

Subgroups — C22×C52⋊#4294 #30685613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅²⋊#4294 #30685613