Group #18013204 — subgroups

Subgroups — C₁₉×#7245 #18013204

Order 4864.

200 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2150	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1567	C₂	1	2	yes	maximal
3	C₂×C₁₉×M₃₂	C₄	1	2	yes	—
4	C₁₉×#423	—	2	2	no	—
5	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×C₄⋊C₁₆	—	2	2	no	—
7	C₁₉×#335	—	2	2	no	—
8	C₁₉×#335	C₄	1	4	yes	—
9	C₂×M₁₆×C₁₉	—	4	2	no	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₁₉×M₃₂	—	4	2	no	—
14	C₂×C₁₆×C₁₉	—	2	2	no	—
15	C₁₉×C₄⋊C₈	—	2	4	no	—
16	C₁₉×C₄⋊C₈	—	4	2	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
21	M₁₆×C₁₉	—	8	4	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	—	4	4	no	—
26	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
27	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
29	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
30	C₄²×C₁₉	D₈	1	1	yes	characteristic
31	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
32	C₁₆×C₁₉	—	4	2	no	—
33	#7245	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₁₉	#106	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	—	2	2	no	—
39	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#102	1	2	yes	—
41	C₂×C₄×C₁₉	#103	1	2	yes	—
42	C₂×C₄×C₁₉	#107	1	1	yes	characteristic
43	C₈×C₁₉	—	2	2	no	—
44	C₈×C₁₉	—	2	1	no	—
45	C₈×C₁₉	—	8	4	no	—
46	C₈×C₁₉	#100	1	1	yes	characteristic
47	C₈×C₁₉	#101	1	1	yes	characteristic
48	#2150	C₂×C₁₉	1	1	yes	characteristic
49	#1567	C₂×C₁₉	1	2	yes	—
50	C₂²×C₁₉	—	2	1	no	—
51	C₂²×C₁₉	—	2	2	no	—
52	C₂²×C₁₉	#340	1	1	yes	characteristic
53	C₄×C₁₉	—	2	1	no	—
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	#338	1	1	yes	characteristic
56	C₄×C₁₉	#343	1	1	yes	characteristic
57	C₄×C₁₉	#361	1	2	yes	—
58	C₄×C₁₉	#362	1	2	yes	—
59	C₂×M₃₂	C₄×C₁₉	1	2	yes	—
60	#423	—	2	2	no	—
61	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
62	C₄⋊C₁₆	—	2	2	no	—
63	#335	—	2	2	no	—
64	#335	C₄×C₁₉	1	4	yes	—
65	C₂×C₁₉	—	4	1	no	—
66	C₂×C₁₉	#1292	1	1	yes	characteristic
67	C₂×C₁₉	#1387	1	2	yes	—
68	C₂×M₁₆	—	4	2	no	—
69	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
70	C₂²×C₈	Q₈×C₁₉	1	1	yes	characteristic
71	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
72	M₃₂	—	4	2	no	—
73	C₂×C₁₆	—	2	2	no	—
74	C₄⋊C₈	—	2	4	no	—
75	C₄⋊C₈	—	4	2	no	—
76	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
77	C₄×C₈	D₄×C₁₉	1	2	yes	—
78	C₁₉	#7245	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
80	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
81	M₁₆	—	8	4	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	4	1	no	—
85	C₂×C₈	—	4	4	no	—
86	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
87	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
88	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
89	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
90	C₄²	D₈×C₁₉	1	1	yes	characteristic
91	C₄²	Q₁₆×C₁₉	1	1	yes	characteristic
92	C₁₆	—	4	2	no	—
93	C₂³	C₁₉×#106	1	1	yes	characteristic
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
99	C₂×C₄	C₁₉×#102	1	2	yes	—
100	C₂×C₄	C₁₉×#103	1	2	yes	—
101	C₂×C₄	C₁₉×#107	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	—	2	2	no	—
104	C₈	—	8	4	no	—
105	C₈	C₁₉×#100	1	1	yes	characteristic
106	C₈	C₁₉×#101	1	1	yes	characteristic
107	C₂²	—	2	2	no	—
108	C₂²	—	2	1	no	—
109	C₂²	C₁₉×#340	1	1	yes	characteristic
110	C₄	—	2	2	no	—
111	C₄	—	2	1	no	—
112	C₄	C₁₉×#338	1	1	yes	characteristic
113	C₄	C₁₉×#343	1	1	yes	characteristic
114	C₄	C₁₉×#361	1	2	yes	—
115	C₄	C₁₉×#362	1	2	yes	—
116	C₂	—	4	1	no	—
117	C₂	C₁₉×#1292	1	1	yes	characteristic
118	C₂	C₁₉×#1387	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2150

C₂

yes

maximal, characteristic

C₁₉×#1567

C₂

yes

maximal

C₂×C₁₉×M₃₂

C₄

yes

—

C₁₉×#423

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×#335

—

C₁₉×#335

C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

SD₁₆

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₁₆×C₁₉

—

#7245

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#106

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#107

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

#1567

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#340

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#362

yes

—

C₂×M₃₂

C₄×C₁₉

yes

—

#423

—

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

—

#335

—

#335

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

#1292

yes

characteristic

C₂×C₁₉

#1387

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₈

Q₈×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

D₄×C₁₉

yes

—

C₁₉

#7245

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

C₂²×C₄

SD₁₆×C₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

C₄²

C₂²⋊C₄×C₁₉

yes

—

C₄²

D₈×C₁₉

yes

characteristic

C₄²

Q₁₆×C₁₉

yes

characteristic

C₁₆

—

C₂³

C₁₉×#106

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×#95

yes

characteristic

C₂×C₄

C₁₉×#102

yes

—

100

C₂×C₄

C₁₉×#103

yes

—

101

C₂×C₄

C₁₉×#107

yes

characteristic

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

C₁₉×#100

yes

characteristic

106

C₈

C₁₉×#101

yes

characteristic

107

C₂²

—

108

C₂²

—

109

C₂²

C₁₉×#340

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

C₁₉×#338

yes

characteristic

113

C₄

C₁₉×#343

yes

characteristic

114

C₄

C₁₉×#361

yes

—

115

C₄

C₁₉×#362

yes

—

116

C₂

—

117

C₂

C₁₉×#1292

yes

characteristic

118

C₂

C₁₉×#1387

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#340
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#340

commutator

C₂×C₈

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₉

prime radical

C₂³×C₁₉

#106

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
33. #7245	C₁₉	direct (N × H)
78. C₁₉	#7245	direct (N × H)

H ≅ G/N

type

33. #7245

C₁₉

direct (N × H)

78. C₁₉

#7245

direct (N × H)

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

subgroup	index
C₁₉×#2150	2
C₁₉×#1567	2
#7245	19

subgroup

index

C₁₉×#2150

C₁₉×#1567

#7245

Subgroups — C₁₉×#7245 #18013204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7245 #18013204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7245 #18013204