Subgroups — C₂×#22555511 #30685570

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	1	yes	maximal, characteristic, complemented
2	#22555511	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅²×D₁₉	C₃	1	1	yes	maximal, characteristic
4	C₅²⋊#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×D₁₉	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₅²×D₁₉	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₃×C₅×D₁₉	—	3	2	no	—
10	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
11	C₅²×D₁₉	C₂×C₉	1	2	yes	complemented
12	C₂²×C₅²⋊C₉	—	19	1	no	maximal, Hall
13	C₂×#4294⋊C₂	—	25	1	no	maximal, Hall
14	C₂×C₃×C₅×C₁₉	—	3	2	no	—
15	C₃×C₅×D₁₉	—	3	4	no	—
16	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅²⋊C₉	—	19	2	no	—
18	C₂×C₅²⋊C₉	—	19	1	no	—
19	C₂×C₅×D₁₉	—	3	2	no	—
20	C₂×#4294	—	25	1	no	—
21	#4294⋊C₂	—	25	2	no	—
22	C₂²×C₃×C₅²	—	57	1	no	—
23	C₃×C₅×C₁₉	—	3	2	no	—
24	C₂×C₃×D₁₉	C₅²⋊C₃	1	1	yes	characteristic
25	C₅²⋊C₉	—	19	1	no	Hall
26	C₂×C₅×C₁₉	—	3	2	no	—
27	C₅×D₁₉	—	3	4	no	—
28	#4294	—	25	1	no	Hall
29	C₂×C₃×C₅²	—	57	2	no	—
30	C₂×C₃×C₅²	D₁₉⋊C₃	1	1	yes	characteristic
31	C₂×C₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic
32	C₃×D₁₉	C₂×C₅²⋊C₃	1	2	yes	—
33	C₂²×C₅²	—	57	1	no	Hall
34	C₅×C₁₉	—	3	2	no	—
35	C₂×D₁₉	C₅²⋊C₉	1	1	yes	characteristic, complemented, Hall
36	C₃×C₅²	C₂×D₁₉⋊C₃	1	1	yes	characteristic
37	C₂²×C₃×C₅	—	57	2	no	—
38	C₃×C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic
39	C₂×C₅²	—	57	2	no	—
40	C₂×C₅²	#4294⋊C₂	1	1	yes	characteristic, complemented
41	C₂×C₁₉	C₂×C₅²⋊C₉	1	1	yes	characteristic, complemented
42	D₁₉	C₂×C₅²⋊C₉	1	2	yes	complemented
43	C₂²×C₉	—	475	1	no	Hall
44	C₂×C₃×C₅	—	3	2	no	—
45	C₂×C₃×C₅	—	57	4	no	—
46	C₅²	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₅	—	57	2	no	—
48	C₁₉	C₂²×C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₉	—	475	2	no	—
50	C₂×C₉	—	475	1	no	—
51	C₃×C₅	—	3	2	no	—
52	C₂²×C₃	—	57	1	no	—
53	C₂×C₅	—	3	2	no	—
54	C₂×C₅	—	57	4	no	—
55	C₉	—	475	1	no	Sylow
56	C₂×C₃	—	57	2	no	—
57	C₂×C₃	D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic
58	C₅	—	3	2	no	—
59	C₂²	—	57	1	no	Sylow
60	C₃	C₂×D₁₉⋊(C₅²⋊C₃)	1	1	yes	characteristic
61	C₂	—	57	2	no	—
62	C₂	#22555511	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₉⋊(C₅²⋊C₃)
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×D₁₉⋊(C₅²⋊C₃)
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₅²×D₁₉	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊#4294	C₂	semidirect
2. #22555511	C₂	direct (N × H)
4. C₅²⋊#4294	C₂²	semidirect
7. C₂×C₅²×D₁₉	C₉	semidirect
10. C₂×C₅²×C₁₉	C₂×C₉	semidirect
11. C₅²×D₁₉	C₂×C₉	semidirect
16. C₅²×C₁₉	C₂²×C₉	semidirect
35. C₂×D₁₉	C₅²⋊C₉	semidirect
40. C₂×C₅²	#4294⋊C₂	semidirect
41. C₂×C₁₉	C₂×C₅²⋊C₉	semidirect
42. D₁₉	C₂×C₅²⋊C₉	semidirect
46. C₅²	C₂×#4294⋊C₂	semidirect
48. C₁₉	C₂²×C₅²⋊C₉	semidirect
62. C₂	#22555511	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
#22555511	2
C₂×C₃×C₅²×D₁₉	3
C₂²×C₅²⋊C₉	19
C₂×#4294⋊C₂	25

Subgroups — C2×#22555511 #30685570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22555511 #30685570