Subgroups — C₂×C₁₉⋊#90646 #30685565

Order 17100.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉⋊#90646	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₂₈₅	—	3	1	no	maximal
4	C₁₉×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅×D₂₈₅	—	3	2	no	—
6	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic
7	C₂×C₅×D₉₅	—	9	1	no	Hall
8	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
9	C₂×D₂₈₅	—	3	1	no	—
10	C₂×C₅×D₅₇	—	15	1	no	—
11	C₂×C₅²×C₁₉	D₉	1	1	yes	characteristic, complemented
12	C₅×D₉₅	—	9	2	no	—
13	C₂×#90646	—	19	1	no	maximal, Hall
14	C₂×D₁₇₁	—	25	1	no	maximal, Hall
15	C₂×C₃×C₅×C₁₉	—	6	1	no	—
16	C₂×C₃×C₅×C₁₉	—	6	1	no	—
17	D₂₈₅	—	3	2	no	—
18	C₅×D₅₇	—	15	2	no	—
19	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅²⋊C₉	D₁₉	1	1	yes	characteristic, complemented
21	#90646	—	19	2	no	—
22	C₂×D₉₅	—	9	1	no	—
23	C₂×C₅×D₁₉	—	45	1	no	—
24	C₂×C₉×C₁₉	—	50	1	no	—
25	D₁₇₁	—	25	2	no	—
26	C₂×C₅×D₁₅	—	57	1	no	—
27	C₃×C₅×C₁₉	—	6	1	no	—
28	C₃×C₅×C₁₉	—	6	1	no	—
29	C₂×D₅₇	—	15	1	no	—
30	C₅²⋊C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₁₉	—	6	1	no	—
32	C₂×C₅×C₁₉	—	6	1	no	—
33	D₉₅	—	9	2	no	—
34	C₅×D₁₉	—	45	2	no	—
35	C₉×C₁₉	—	50	1	no	Hall
36	C₂×C₃×C₅²	D₅₇	1	1	yes	characteristic
37	C₅×D₁₅	—	57	2	no	—
38	C₂×C₃×C₁₉	#3874	1	1	yes	characteristic
39	D₅₇	—	15	2	no	—
40	C₂×C₅×D₅	—	171	1	no	Hall
41	C₅×C₁₉	—	6	1	no	—
42	C₅×C₁₉	—	6	1	no	—
43	C₂×D₁₉	—	45	1	no	Hall
44	C₃×C₅²	C₂×D₅₇	1	1	yes	characteristic
45	C₂×D₁₅	—	57	1	no	—
46	C₂×C₅×D₃	—	285	1	no	—
47	C₃×C₁₉	C₂×#3874	1	1	yes	characteristic
48	C₂×C₅²	D₁₇₁	1	1	yes	characteristic, complemented
49	C₅×D₅	—	171	2	no	—
50	C₂×C₁₉	#90646	1	1	yes	characteristic, complemented
51	D₁₉	—	45	2	no	—
52	C₂×D₉	—	475	1	no	Hall
53	C₂×C₃×C₅	—	6	1	no	—
54	C₂×C₃×C₅	—	6	1	no	—
55	D₁₅	—	57	2	no	—
56	C₅×D₃	—	285	2	no	—
57	C₅²	C₂×D₁₇₁	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₅	—	855	1	no	—
59	C₂×D₅	—	171	1	no	—
60	C₁₉	C₂×#90646	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₉	—	25	1	no	—
62	D₉	—	475	2	no	—
63	C₃×C₅	—	6	1	no	—
64	C₃×C₅	—	6	1	no	—
65	C₂×D₃	—	285	1	no	—
66	C₂×C₅	—	3	1	no	—
67	C₂×C₅	—	6	1	no	—
68	C₂×C₅	—	855	2	no	—
69	D₅	—	171	2	no	—
70	C₉	—	25	1	no	Sylow
71	C₂×C₃	C₁₉⋊#3874	1	1	yes	characteristic
72	D₃	—	285	2	no	—
73	C₅	—	3	1	no	—
74	C₅	—	6	1	no	—
75	C₂²	—	855	1	no	Sylow
76	C₃	C₂×C₁₉⋊#3874	1	1	yes	characteristic
77	C₂	—	855	2	no	—
78	C₂	C₁₉⋊#90646	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊#90646
commutator, cosocle, hypocenter	C₁₉×C₅²⋊C₉	C₂²
Frattini	C₃	C₂×C₁₉⋊#3874
Fitting, socle	C₂×C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₁₉×C₅²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×C₅²⋊C₉	C₂	semidirect
2. C₁₉⋊#90646	C₂	direct (N × H)
4. C₁₉×C₅²⋊C₉	C₂²	semidirect
11. C₂×C₅²×C₁₉	D₉	semidirect
19. C₅²×C₁₉	C₂×D₉	semidirect
20. C₂×C₅²⋊C₉	D₁₉	semidirect
30. C₅²⋊C₉	C₂×D₁₉	semidirect
48. C₂×C₅²	D₁₇₁	semidirect
50. C₂×C₁₉	#90646	semidirect
57. C₅²	C₂×D₁₇₁	semidirect
60. C₁₉	C₂×#90646	semidirect
78. C₂	C₁₉⋊#90646	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×C₁₉×C₅²⋊C₉	2
C₁₉⋊#90646	2
C₂×C₅×D₂₈₅	3
C₂×#90646	19
C₂×D₁₇₁	25

Subgroups — C2×C19⋊#90646 #30685565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉⋊#90646 #30685565