Subgroups — C₂×#22555535 #30685728

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊#4296	C₂	1	1	yes	maximal, characteristic, complemented
2	#22555535	C₂	1	1	yes	maximal, characteristic, direct product factor
3	#22555535	C₂	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₅⋊(C₅⋊(D₁₉⋊C₃))	C₃	1	1	yes	maximal, characteristic
5	C₅²⋊#4296	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅²×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₅⋊(C₅⋊(D₁₉⋊C₃))	C₂×C₃	1	1	yes	characteristic
8	C₅⋊(C₅⋊(D₁₉⋊C₃))	C₂×C₃	1	1	yes	characteristic
9	C₂×C₅⋊D₉₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₅²×C₁₉⋊C₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×C₅⋊(D₁₉⋊C₃)	—	15	2	no	—
12	C₂×C₅²×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅⋊D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×(C₅⋊D₅)⋊C₉	—	19	1	no	maximal, Hall
16	C₂×AGL(1,𝔽₁₉)	—	25	1	no	maximal, Hall
17	C₂×C₅×C₁₉⋊C₃	—	3	2	no	—
18	C₅⋊(D₁₉⋊C₃)	—	15	2	no	—
19	C₅⋊(D₁₉⋊C₃)	—	15	2	no	—
20	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅²⋊C₉	—	19	1	no	—
22	(C₅⋊D₅)⋊C₉	—	19	1	no	—
23	(C₅⋊D₅)⋊C₉	—	19	1	no	—
24	C₂×D₉₅	—	15	2	no	—
25	C₂×#4296	—	25	1	no	—
26	AGL(1,𝔽₁₉)	—	25	1	no	—
27	AGL(1,𝔽₁₉)	—	25	1	no	—
28	C₂×C₃×C₅⋊D₅	—	19	1	no	—
29	C₅×C₁₉⋊C₃	—	3	2	no	—
30	C₂×D₁₉⋊C₃	—	75	1	no	—
31	C₅²⋊C₉	—	19	1	no	Hall
32	C₂×C₅×C₁₉	—	3	2	no	—
33	D₉₅	—	15	2	no	—
34	D₉₅	—	15	2	no	—
35	#4296	—	25	1	no	Hall
36	C₂×C₃×C₅²	—	19	1	no	—
37	C₃×C₅⋊D₅	—	19	1	no	—
38	C₃×C₅⋊D₅	—	19	1	no	—
39	C₂×C₁₉⋊C₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
40	D₁₉⋊C₃	—	75	1	no	—
41	D₁₉⋊C₃	—	75	1	no	—
42	C₂×C₅⋊D₅	—	171	1	no	Hall
43	C₅×C₁₉	—	3	2	no	—
44	C₂×D₁₉	—	75	1	no	Hall
45	C₃×C₅²	—	19	1	no	—
46	C₂×C₃×D₅	—	285	2	no	—
47	C₁₉⋊C₃	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
48	C₂×C₅²	AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented
49	C₅⋊D₅	—	171	1	no	—
50	C₅⋊D₅	—	171	1	no	—
51	C₂×C₁₉	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented
52	D₁₉	—	75	1	no	—
53	D₁₉	—	75	1	no	—
54	C₂²×C₉	—	475	1	no	Hall
55	C₂×C₃×C₅	—	57	2	no	—
56	C₃×D₅	—	285	2	no	—
57	C₃×D₅	—	285	2	no	—
58	C₅²	C₂×AGL(1,𝔽₁₉)	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₅	—	855	2	no	—
60	C₁₉	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₉	—	475	1	no	—
62	C₂×C₉	—	475	1	no	—
63	C₂×C₉	—	475	1	no	—
64	C₃×C₅	—	57	2	no	—
65	C₂²×C₃	—	1425	1	no	—
66	C₂×C₅	—	3	2	no	—
67	D₅	—	855	2	no	—
68	D₅	—	855	2	no	—
69	C₉	—	475	1	no	Sylow
70	C₂×C₃	—	19	1	no	—
71	C₂×C₃	—	1425	1	no	—
72	C₂×C₃	—	475	1	no	—
73	C₅	—	3	2	no	—
74	C₂²	—	4275	1	no	Sylow
75	C₃	—	19	1	no	—
76	C₂	—	4275	1	no	—
77	C₂	—	4275	1	no	—
78	C₂	#22555535	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#22555535
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical	C₂×C₅⋊(C₅⋊(D₁₉⋊C₃))	C₃
cosocle	C₅²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²⋊#4296	C₂	semidirect
2. #22555535	C₂	direct (N × H)
3. #22555535	C₂	direct (N × H)
5. C₅²⋊#4296	C₂²	semidirect
9. C₂×C₅⋊D₉₅	C₉	semidirect
12. C₂×C₅²×C₁₉	C₂×C₉	semidirect
13. C₅⋊D₉₅	C₂×C₉	semidirect
14. C₅⋊D₉₅	C₂×C₉	semidirect
20. C₅²×C₁₉	C₂²×C₉	semidirect
48. C₂×C₅²	AGL(1,𝔽₁₉)	semidirect
51. C₂×C₁₉	(C₅⋊D₅)⋊C₉	semidirect
58. C₅²	C₂×AGL(1,𝔽₁₉)	semidirect
60. C₁₉	C₂×(C₅⋊D₅)⋊C₉	semidirect
78. C₂	#22555535	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⋊#4296	2
#22555535	2
C₂×C₅⋊(C₅⋊(D₁₉⋊C₃))	3
C₂×(C₅⋊D₅)⋊C₉	19
C₂×AGL(1,𝔽₁₉)	25

Subgroups — C2×#22555535 #30685728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22555535 #30685728