Group #16815334 — subgroups

Subgroups — C₂₉×#1620 #16815334

Order 3712.

240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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	C₂₉×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#493	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#460	C₂	1	2	yes	maximal, complemented
4	C₂₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×SD₁₆×C₂₉	—	2	2	no	—
7	C₂×D₈×C₂₉	—	2	2	no	—
8	C₂₉×#127	C₂²	1	1	yes	characteristic
9	C₂₉×#127	C₂²	1	1	yes	characteristic
10	C₂₉×#124	—	2	2	no	—
11	C₂₉×#123	—	2	2	no	—
12	C₄×Q₈×C₂₉	C₂²	1	2	yes	—
13	C₄×D₄×C₂₉	—	2	2	no	—
14	C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂₉×#102	—	2	2	no	—
16	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₂₉	D₄	1	2	yes	—
18	C₂×D₄×C₂₉	—	2	2	no	—
19	C₂×D₄×C₂₉	—	2	1	no	—
20	C₂×D₄×C₂₉	—	2	2	no	—
21	C₂×D₄×C₂₉	D₄	1	2	yes	—
22	C₂²×C₄×C₂₉	—	2	2	no	—
23	SD₁₆×C₂₉	—	4	4	no	—
24	D₈×C₂₉	—	4	4	no	—
25	C₂×C₈×C₂₉	—	2	1	no	—
26	C₂×C₈×C₂₉	—	2	2	no	—
27	C₄⋊C₄×C₂₉	—	2	2	no	—
28	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
29	C₂²⋊C₄×C₂₉	—	2	4	no	—
30	C₂²⋊C₄×C₂₉	—	2	2	no	—
31	C₄²×C₂₉	—	2	2	no	—
32	C₄²×C₂₉	C₂³	1	1	yes	characteristic
33	C₂³×C₂₉	—	2	2	no	—
34	C₂³×C₂₉	—	4	1	no	—
35	Q₈×C₂₉	—	2	2	no	—
36	Q₈×C₂₉	—	2	2	no	—
37	D₄×C₂₉	—	4	2	no	—
38	D₄×C₂₉	—	4	2	no	—
39	D₄×C₂₉	—	4	2	no	—
40	D₄×C₂₉	—	4	2	no	—
41	D₄×C₂₉	—	4	2	no	—
42	D₄×C₂₉	—	4	2	no	—
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	2	2	no	—
45	C₂×C₄×C₂₉	—	8	2	no	—
46	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
48	C₈×C₂₉	—	2	2	no	—
49	C₈×C₂₉	—	4	2	no	—
50	#1620	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂²×C₂₉	—	4	4	no	—
52	C₂²×C₂₉	—	4	2	no	—
53	C₂²×C₂₉	—	8	2	no	—
54	C₂²×C₂₉	—	8	1	no	—
55	C₂²×C₂₉	#120	1	1	yes	characteristic
56	C₄×C₂₉	—	2	1	no	—
57	C₄×C₂₉	—	4	2	no	—
58	C₄×C₂₉	—	4	2	no	—
59	C₄×C₂₉	#135	1	2	yes	—
60	C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
61	#559	C₂×C₂₉	1	1	yes	characteristic, complemented
62	#493	C₂×C₂₉	1	1	yes	characteristic
63	#460	C₂×C₂₉	1	2	yes	complemented
64	#331	C₂×C₂₉	1	1	yes	characteristic, complemented
65	Q₈⋊C₈	C₂×C₂₉	1	2	yes	complemented
66	C₂×C₂₉	—	8	2	no	—
67	C₂×C₂₉	—	16	1	no	—
68	C₂×C₂₉	#449	1	2	yes	—
69	C₂×C₂₉	#453	1	1	yes	characteristic
70	C₂×SD₁₆	—	2	2	no	—
71	C₂×D₈	—	2	2	no	—
72	#127	C₂²×C₂₉	1	1	yes	characteristic
73	#127	C₂²×C₂₉	1	1	yes	characteristic
74	#124	—	2	2	no	—
75	#123	—	2	2	no	—
76	C₄×Q₈	C₂²×C₂₉	1	2	yes	—
77	C₄×D₄	—	2	2	no	—
78	C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
79	#102	—	2	2	no	—
80	C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
81	C₂₉	#1620	1	1	yes	characteristic, direct product factor, Sylow
82	C₂×Q₈	D₄×C₂₉	1	2	yes	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	—	2	1	no	—
86	C₂×D₄	D₄×C₂₉	1	2	yes	—
87	C₂²×C₄	—	2	2	no	—
88	SD₁₆	—	4	4	no	—
89	D₈	—	4	4	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	2	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
94	C₂²⋊C₄	—	2	4	no	—
95	C₂²⋊C₄	—	2	2	no	—
96	C₄²	—	2	2	no	—
97	C₄²	C₂³×C₂₉	1	1	yes	characteristic
98	C₂³	—	2	2	no	—
99	C₂³	—	4	1	no	—
100	Q₈	—	2	2	no	—
101	Q₈	—	2	2	no	—
102	D₄	—	4	2	no	—
103	D₄	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	4	2	no	—
106	D₄	—	4	2	no	—
107	D₄	—	4	2	no	—
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	8	2	no	—
111	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
112	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
113	C₈	—	2	2	no	—
114	C₈	—	4	2	no	—
115	C₂²	—	4	4	no	—
116	C₂²	—	4	2	no	—
117	C₂²	—	8	2	no	—
118	C₂²	—	8	1	no	—
119	C₂²	C₂₉×#120	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	4	2	no	—
122	C₄	—	4	2	no	—
123	C₄	C₂₉×#135	1	2	yes	—
124	C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
125	C₂	—	8	2	no	—
126	C₂	—	16	1	no	—
127	C₂	C₂₉×#449	1	2	yes	—
128	C₂	C₂₉×#453	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#559

C₂

yes

maximal, characteristic, complemented

C₂₉×#493

C₂

yes

maximal, characteristic

C₂₉×#460

C₂

yes

maximal, complemented

C₂₉×#331

C₂

yes

maximal, characteristic, complemented

C₂₉×Q₈⋊C₈

C₂

yes

maximal, complemented

C₂×SD₁₆×C₂₉

—

C₂×D₈×C₂₉

—

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#127

C₂²

yes

characteristic

C₂₉×#124

—

C₂₉×#123

—

C₄×Q₈×C₂₉

C₂²

yes

—

C₄×D₄×C₂₉

—

C₂₉×C₄⋊C₈

C₂²

yes

—

C₂₉×#102

—

C₄×C₈×C₂₉

C₂²

yes

characteristic

C₂×Q₈×C₂₉

D₄

yes

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

—

SD₁₆×C₂₉

—

D₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

C₂³

yes

characteristic

C₂³×C₂₉

—

C₂³×C₂₉

—

Q₈×C₂₉

—

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

#1620

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#120

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#135

yes

—

C₄×C₂₉

AGL(1,ℤ/8)

yes

—

#559

C₂×C₂₉

yes

characteristic, complemented

#493

C₂×C₂₉

yes

characteristic

#460

C₂×C₂₉

yes

complemented

#331

C₂×C₂₉

yes

characteristic, complemented

Q₈⋊C₈

C₂×C₂₉

yes

complemented

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#449

yes

—

C₂×C₂₉

#453

yes

characteristic

C₂×SD₁₆

—

C₂×D₈

—

#127

C₂²×C₂₉

yes

characteristic

#127

C₂²×C₂₉

yes

characteristic

#124

—

#123

—

C₄×Q₈

C₂²×C₂₉

yes

—

C₄×D₄

—

C₄⋊C₈

C₂²×C₂₉

yes

—

#102

—

C₄×C₈

C₂²×C₂₉

yes

characteristic

C₂₉

#1620

yes

characteristic, direct product factor, Sylow

C₂×Q₈

D₄×C₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

D₄×C₂₉

yes

—

C₂²×C₄

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₂₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂³×C₂₉

yes

characteristic

C₂³

—

C₂³

—

100

Q₈

—

101

Q₈

—

102

D₄

—

103

D₄

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

112

C₂×C₄

C₂×D₄×C₂₉

yes

—

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₂₉×#120

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

C₂₉×#135

yes

—

124

C₄

C₂₉×AGL(1,ℤ/8)

yes

—

125

C₂

—

126

C₂

—

127

C₂

C₂₉×#449

yes

—

128

C₂

C₂₉×#453

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₂₉
prime radical	C₂₉×#493	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#120

commutator, Frattini, cosocle

C₄²

C₂³×C₂₉

prime radical

C₂₉×#493

C₂

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

N	H ≅ G/N	type
1. C₂₉×#559	C₂	semidirect
3. C₂₉×#460	C₂	semidirect
4. C₂₉×#331	C₂	semidirect
5. C₂₉×Q₈⋊C₈	C₂	semidirect
50. #1620	C₂₉	direct (N × H)
61. #559	C₂×C₂₉	semidirect
63. #460	C₂×C₂₉	semidirect
64. #331	C₂×C₂₉	semidirect
65. Q₈⋊C₈	C₂×C₂₉	semidirect
81. C₂₉	#1620	direct (N × H)

H ≅ G/N

type

1. C₂₉×#559

C₂

semidirect

3. C₂₉×#460

C₂

semidirect

4. C₂₉×#331

C₂

semidirect

5. C₂₉×Q₈⋊C₈

C₂

semidirect

50. #1620

C₂₉

direct (N × H)

61. #559

C₂×C₂₉

semidirect

63. #460

C₂×C₂₉

semidirect

64. #331

C₂×C₂₉

semidirect

65. Q₈⋊C₈

C₂×C₂₉

semidirect

81. C₂₉

#1620

direct (N × H)

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

subgroup	index
C₂₉×#559	2
C₂₉×#493	2
C₂₉×#460	2
C₂₉×#331	2
C₂₉×Q₈⋊C₈	2
#1620	29

subgroup

index

C₂₉×#559

C₂₉×#493

C₂₉×#460

C₂₉×#331

C₂₉×Q₈⋊C₈

#1620

Subgroups — C₂₉×#1620 #16815334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#1620 #16815334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1620 #16815334