Group #20302170 — subgroups

Subgroups — C₂₉×#7270 #20302170

Order 7424.

208 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 114 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	C₂×C₂₉×#364	C₂	1	2	yes	maximal
2	C₂₉×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×M₃₂	—	2	2	no	—
4	C₂×C₂₉×#108	—	2	2	no	—
5	C₂₉×#423	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#364	—	2	2	no	—
8	C₂₉×#364	C₄	1	4	yes	—
9	C₂×M₁₆×C₂₉	—	2	2	no	—
10	C₂²×C₈×C₂₉	D₄	1	2	yes	—
11	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂₉×M₃₂	—	2	4	no	—
13	C₂₉×M₃₂	—	4	2	no	—
14	C₂×C₁₆×C₂₉	—	4	2	no	—
15	C₂₉×#108	—	4	2	no	—
16	C₂₉×#108	—	4	2	no	—
17	C₂₉×C₄⋊C₈	—	4	2	no	—
18	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₂₉	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	—	2	1	no	—
22	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	M₁₆×C₂₉	—	4	4	no	—
24	C₂×C₈×C₂₉	—	4	2	no	—
25	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈×C₂₉	C₄⋊C₄	1	2	yes	—
27	C₂×C₈×C₂₉	D₈	1	2	yes	—
28	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
29	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
30	C₂×C₈×C₂₉	Q₁₆	1	2	yes	—
31	C₄²×C₂₉	—	2	1	no	—
32	C₄²×C₂₉	C₄²	1	1	yes	characteristic
33	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
34	C₁₆×C₂₉	—	4	4	no	—
35	#7270	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂³×C₂₉	#101	1	1	yes	characteristic
37	C₂×C₄×C₂₉	—	2	1	no	—
38	C₂×C₄×C₂₉	—	2	1	no	—
39	C₂×C₄×C₂₉	—	4	2	no	—
40	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#100	1	1	yes	characteristic
42	C₂×C₄×C₂₉	#102	1	2	yes	—
43	C₂×C₄×C₂₉	#103	1	2	yes	—
44	C₈×C₂₉	—	8	2	no	—
45	C₈×C₂₉	#102	1	2	yes	—
46	C₈×C₂₉	#103	1	2	yes	—
47	C₈×C₂₉	#106	1	2	yes	—
48	C₈×C₂₉	#107	1	2	yes	—
49	C₂×#364	C₂×C₂₉	1	2	yes	—
50	#1848	C₂×C₂₉	1	1	yes	characteristic
51	C₂²×C₂₉	—	4	1	no	—
52	C₂²×C₂₉	#332	1	2	yes	—
53	C₂²×C₂₉	#343	1	1	yes	characteristic
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	—	4	1	no	—
56	C₄×C₂₉	#331	1	1	yes	characteristic
57	C₄×C₂₉	#333	1	1	yes	characteristic
58	C₄×C₂₉	#340	1	2	yes	—
59	C₂×M₃₂	—	2	2	no	—
60	C₂×#108	—	2	2	no	—
61	#423	C₄×C₂₉	1	2	yes	—
62	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
63	#364	—	2	2	no	—
64	#364	C₄×C₂₉	1	4	yes	—
65	C₂×C₂₉	—	2	1	no	—
66	C₂×C₂₉	—	2	2	no	—
67	C₂×C₂₉	#1296	1	1	yes	characteristic
68	C₂×M₁₆	—	2	2	no	—
69	C₂²×C₈	D₄×C₂₉	1	2	yes	—
70	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
71	M₃₂	—	2	4	no	—
72	M₃₂	—	4	2	no	—
73	C₂×C₁₆	—	4	2	no	—
74	#108	—	4	2	no	—
75	#108	—	4	2	no	—
76	C₄⋊C₈	—	4	2	no	—
77	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
78	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
79	C₄×C₈	Q₈×C₂₉	1	1	yes	characteristic
80	C₂₉	#7270	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₄	—	2	1	no	—
82	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
83	M₁₆	—	4	4	no	—
84	C₂×C₈	—	4	2	no	—
85	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
86	C₂×C₈	C₄⋊C₄×C₂₉	1	2	yes	—
87	C₂×C₈	D₈×C₂₉	1	2	yes	—
88	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
89	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
90	C₂×C₈	Q₁₆×C₂₉	1	2	yes	—
91	C₄²	—	2	1	no	—
92	C₄²	C₄²×C₂₉	1	1	yes	characteristic
93	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
94	C₁₆	—	4	4	no	—
95	C₂³	C₂₉×#101	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
100	C₂×C₄	C₂₉×#100	1	1	yes	characteristic
101	C₂×C₄	C₂₉×#102	1	2	yes	—
102	C₂×C₄	C₂₉×#103	1	2	yes	—
103	C₈	—	8	2	no	—
104	C₈	C₂₉×#102	1	2	yes	—
105	C₈	C₂₉×#103	1	2	yes	—
106	C₈	C₂₉×#106	1	2	yes	—
107	C₈	C₂₉×#107	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	C₂₉×#332	1	2	yes	—
110	C₂²	C₂₉×#343	1	1	yes	characteristic
111	C₄	—	2	2	no	—
112	C₄	—	4	1	no	—
113	C₄	C₂₉×#331	1	1	yes	characteristic
114	C₄	C₂₉×#333	1	1	yes	characteristic
115	C₄	C₂₉×#340	1	2	yes	—
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	C₂₉×#1296	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₂₉×#364

C₂

yes

maximal

C₂₉×#1848

C₂

yes

maximal, characteristic

C₂×C₂₉×M₃₂

—

C₂×C₂₉×#108

—

C₂₉×#423

C₄

yes

—

C₂×C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#364

—

C₂₉×#364

C₄

yes

—

C₂×M₁₆×C₂₉

—

C₂²×C₈×C₂₉

D₄

yes

—

C₂×C₄²×C₂₉

C₂×C₄

yes

characteristic

C₂₉×M₃₂

—

C₂₉×M₃₂

—

C₂×C₁₆×C₂₉

—

C₂₉×#108

—

C₂₉×#108

—

C₂₉×C₄⋊C₈

—

C₄×C₈×C₂₉

C₂×C₄

yes

—

C₄×C₈×C₂₉

D₄

yes

characteristic

C₄×C₈×C₂₉

Q₈

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂²⋊C₄

yes

—

C₂×C₈×C₂₉

C₄⋊C₄

yes

—

C₂×C₈×C₂₉

D₈

yes

—

C₂×C₈×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

SD₁₆

yes

—

C₂×C₈×C₂₉

Q₁₆

yes

—

C₄²×C₂₉

—

C₄²×C₂₉

C₄²

yes

characteristic

C₄²×C₂₉

C₄⋊C₄

yes

characteristic

C₁₆×C₂₉

—

#7270

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₉

#101

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

C₂×C₄×C₂₉

yes

—

C₂×C₄×C₂₉

#103

yes

—

C₈×C₂₉

—

C₈×C₂₉

#102

yes

—

C₈×C₂₉

#103

yes

—

C₈×C₂₉

#106

yes

—

C₈×C₂₉

#107

yes

—

C₂×#364

C₂×C₂₉

yes

—

#1848

C₂×C₂₉

yes

characteristic

C₂²×C₂₉

—

C₂²×C₂₉

#332

yes

—

C₂²×C₂₉

#343

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

yes

C₄×C₂₉

yes

C₄×C₂₉

yes

—

C₂×M₃₂

—

C₂×#108

—

#423

C₄×C₂₉

yes

—

C₂×C₄×C₈

C₂²×C₂₉

yes

characteristic

#364

—

#364

C₄×C₂₉

yes

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#1296

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

D₄×C₂₉

yes

—

C₂×C₄²

C₂×C₄×C₂₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₂₉

yes

—

C₄×C₈

D₄×C₂₉

yes

characteristic

C₄×C₈

Q₈×C₂₉

yes

characteristic

C₂₉

#7270

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²⋊C₄×C₂₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₂₉

yes

—

C₂×C₈

C₄⋊C₄×C₂₉

yes

—

C₂×C₈

D₈×C₂₉

yes

—

C₂×C₈

SD₁₆×C₂₉

yes

—

C₂×C₈

SD₁₆×C₂₉

yes

—

C₂×C₈

Q₁₆×C₂₉

yes

—

C₄²

—

C₄²

C₄²×C₂₉

yes

characteristic

C₄²

C₄⋊C₄×C₂₉

yes

characteristic

C₁₆

—

C₂³

C₂₉×#101

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂₉×#95

yes

characteristic

100

C₂×C₄

C₂₉×#100

yes

characteristic

101

C₂×C₄

C₂₉×#102

yes

—

102

C₂×C₄

C₂₉×#103

yes

—

103

C₈

—

104

C₈

C₂₉×#102

yes

—

105

C₈

C₂₉×#103

yes

—

106

C₈

C₂₉×#106

yes

—

107

C₈

C₂₉×#107

yes

—

108

C₂²

—

109

C₂²

C₂₉×#332

yes

—

110

C₂²

C₂₉×#343

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

C₂₉×#331

yes

characteristic

114

C₄

C₂₉×#333

yes

characteristic

115

C₄

C₂₉×#340

yes

—

116

C₂

—

117

C₂

—

118

C₂

C₂₉×#1296

yes

characteristic

	subgroup	G/H
center	C₄×C₂₉	#331
commutator	C₄²	C₄²×C₂₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₂₉
socle	C₂×C₂₉	#1296
prime radical	C₂³×C₂₉	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

subgroup

G/H

center

C₄×C₂₉

#331

commutator

C₄²

C₄²×C₂₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₂₉

C₂×C₂₉

C₂³×C₂₉

G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

N	H ≅ G/N	type
35. #7270	C₂₉	direct (N × H)
80. C₂₉	#7270	direct (N × H)

H ≅ G/N

type

35. #7270

C₂₉

direct (N × H)

80. C₂₉

#7270

direct (N × H)

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

subgroup	index
C₂×C₂₉×#364	2
C₂₉×#1848	2
#7270	29

subgroup

index

C₂×C₂₉×#364

C₂₉×#1848

#7270

Subgroups — C₂₉×#7270 #20302170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#7270 #20302170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7270 #20302170