Group #13111132 — subgroups

Subgroups — C₁₃×#2074 #13111132

Order 1664.

222 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 92 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×C₁₃×#103	C₂	1	2	yes	maximal
2	C₁₃×#391	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#382	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#340	C₂	1	2	yes	maximal
5	C₁₃×#336	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#103	—	2	4	no	—
12	C₁₃×#95	—	2	2	no	—
13	C₁₃×#95	—	2	2	no	—
14	C₂×Q₈×C₁₃	—	2	1	no	—
15	C₂×Q₈×C₁₃	—	2	2	no	—
16	C₂×Q₈×C₁₃	—	2	2	no	—
17	C₂×Q₈×C₁₃	D₄	1	2	yes	—
18	C₂²×C₄×C₁₃	—	2	1	no	—
19	C₂²×C₄×C₁₃	—	2	2	no	—
20	C₂²×C₄×C₁₃	—	2	1	no	—
21	C₂²×C₄×C₁₃	D₄	1	2	yes	—
22	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×C₈×C₁₃	—	2	2	no	—
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₄²×C₁₃	—	2	2	no	—
30	#2074	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
32	Q₈×C₁₃	—	2	4	no	—
33	Q₈×C₁₃	—	4	2	no	—
34	C₂×C₄×C₁₃	—	2	2	no	—
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	—	2	2	no	—
37	C₂×C₄×C₁₃	—	2	2	no	—
38	C₂×C₄×C₁₃	—	4	1	no	—
39	C₂×C₄×C₁₃	—	4	1	no	—
40	C₂×C₄×C₁₃	—	4	2	no	—
41	C₂×C₄×C₁₃	—	4	1	no	—
42	C₂×C₄×C₁₃	—	4	2	no	—
43	C₂×C₄×C₁₃	—	4	2	no	—
44	C₂×C₄×C₁₃	—	4	2	no	—
45	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₃	#41	1	2	yes	—
47	C₂×C₄×C₁₃	#41	1	2	yes	—
48	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
49	C₈×C₁₃	—	4	2	no	—
50	C₂×#103	C₂×C₁₃	1	2	yes	—
51	#391	C₂×C₁₃	1	1	yes	characteristic
52	#382	C₂×C₁₃	1	1	yes	characteristic
53	#340	C₂×C₁₃	1	2	yes	—
54	#336	C₂×C₁₃	1	1	yes	characteristic
55	C₂²×C₁₃	#121	1	1	yes	characteristic
56	C₂²×C₁₃	#123	1	1	yes	characteristic
57	C₂²×C₁₃	#124	1	1	yes	characteristic
58	C₂²×C₁₃	#135	1	2	yes	—
59	C₂²×C₁₃	#137	1	2	yes	—
60	C₄×C₁₃	—	4	2	no	—
61	C₄×C₁₃	—	4	2	no	—
62	C₄×C₁₃	—	8	2	no	—
63	C₄×C₁₃	—	8	1	no	—
64	C₄×C₁₃	#123	1	2	yes	—
65	C₄×C₁₃	#126	1	2	yes	—
66	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
67	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
68	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
70	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
71	#103	—	2	4	no	—
72	#95	—	2	2	no	—
73	#95	—	2	2	no	—
74	C₂×C₁₃	#397	1	1	yes	characteristic
75	C₂×C₁₃	#464	1	2	yes	—
76	C₂×C₁₃	#485	1	2	yes	—
77	C₂×C₁₃	#488	1	1	yes	characteristic
78	C₂×C₁₃	#491	1	1	yes	characteristic
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	D₄×C₁₃	1	2	yes	—
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	—	2	2	no	—
85	C₂²×C₄	—	2	1	no	—
86	C₂²×C₄	D₄×C₁₃	1	2	yes	—
87	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₄⋊C₄	—	2	2	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	—	2	2	no	—
94	C₄²	—	2	2	no	—
95	C₁₃	#2074	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
97	Q₈	—	2	4	no	—
98	Q₈	—	4	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	2	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	4	2	no	—
110	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
111	C₂×C₄	C₁₃×#41	1	2	yes	—
112	C₂×C₄	C₁₃×#41	1	2	yes	—
113	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
114	C₈	—	4	2	no	—
115	C₂²	C₁₃×#121	1	1	yes	characteristic
116	C₂²	C₁₃×#123	1	1	yes	characteristic
117	C₂²	C₁₃×#124	1	1	yes	characteristic
118	C₂²	C₁₃×#135	1	2	yes	—
119	C₂²	C₁₃×#137	1	2	yes	—
120	C₄	—	4	2	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	2	no	—
123	C₄	—	8	1	no	—
124	C₄	C₁₃×#123	1	2	yes	—
125	C₄	C₁₃×#126	1	2	yes	—
126	C₂	C₁₃×#397	1	1	yes	characteristic
127	C₂	C₁₃×#464	1	2	yes	—
128	C₂	C₁₃×#485	1	2	yes	—
129	C₂	C₁₃×#488	1	1	yes	characteristic
130	C₂	C₁₃×#491	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#103

C₂

yes

maximal

C₁₃×#391

C₂

yes

maximal, characteristic

C₁₃×#382

C₂

yes

maximal, characteristic

C₁₃×#340

C₂

yes

maximal

C₁₃×#336

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₃

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×#103

—

C₁₃×#95

—

C₁₃×#95

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

#2074

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

characteristic

C₈×C₁₃

—

C₂×#103

C₂×C₁₃

yes

—

#391

C₂×C₁₃

yes

characteristic

#382

C₂×C₁₃

yes

characteristic

#340

C₂×C₁₃

yes

—

#336

C₂×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

—

C₂²×C₁₃

#137

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#123

yes

—

C₄×C₁₃

#126

yes

—

C₂²×Q₈

C₂²×C₁₃

yes

characteristic

C₂²×C₈

C₂²×C₁₃

yes

—

C₂×C₄⋊C₄

C₂²×C₁₃

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₃

yes

—

C₂×C₄²

C₂²×C₁₃

yes

—

—

—

C₂×C₁₃

#397

yes

characteristic

C₂×C₁₃

#464

yes

—

C₂×C₁₃

#485

yes

—

C₂×C₁₃

yes

C₂×C₁₃

yes

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₄×C₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₁₃

yes

—

C₂²×C₄

C₂³×C₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₁₃

#2074

yes

characteristic, direct product factor, Sylow

C₂³

C₂×D₄×C₁₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

111

C₂×C₄

C₁₃×#41

yes

—

112

C₂×C₄

C₁₃×#41

yes

—

113

C₂×C₄

C₁₃×#41

yes

characteristic

114

C₈

—

115

C₂²

C₁₃×#121

yes

characteristic

116

C₂²

C₁₃×#123

yes

characteristic

117

C₂²

C₁₃×#124

yes

characteristic

118

C₂²

C₁₃×#135

yes

—

119

C₂²

C₁₃×#137

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

C₁₃×#123

yes

—

125

C₄

C₁₃×#126

yes

—

126

C₂

C₁₃×#397

yes

characteristic

127

C₂

C₁₃×#464

yes

—

128

C₂

C₁₃×#485

yes

—

129

C₂

C₁₃×#488

yes

characteristic

130

C₂

C₁₃×#491

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

C₂×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₁₃

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
30. #2074	C₁₃	direct (N × H)
95. C₁₃	#2074	direct (N × H)

H ≅ G/N

type

30. #2074

C₁₃

direct (N × H)

95. C₁₃

#2074

direct (N × H)

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

subgroup	index
C₂×C₁₃×#103	2
C₁₃×#391	2
C₁₃×#382	2
C₁₃×#340	2
C₁₃×#336	2
#2074	13

subgroup

index

C₂×C₁₃×#103

C₁₃×#391

C₁₃×#382

C₁₃×#340

C₁₃×#336

#2074

Subgroups — C₁₃×#2074 #13111132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#2074 #13111132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2074 #13111132