Group #15696639 — subgroups

Subgroups — C₁₃×#10300 #15696639

Order 3328.

592 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₁₃×#3253	C₂	1	3	yes	maximal, complemented
2	C₁₃×#1962	C₂	1	3	yes	maximal, complemented
3	C₁₃×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#532	C₂²	1	3	yes	—
5	C₁₃×#476	—	2	6	no	—
6	C₁₃×#469	—	2	6	no	—
7	C₁₃×#459	—	2	6	no	—
8	C₁₃×#423	C₂²	1	3	yes	—
9	C₂×C₁₃×#104	—	2	6	no	—
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#41	—	2	3	no	—
12	C₂×C₁₃×D₈	—	2	6	no	—
13	C₂×C₁₃×M₁₆	D₄	1	6	yes	—
14	C₁₃×C₄⋊Q₈	D₄	1	3	yes	—
15	C₁₃×#127	D₄	1	3	yes	—
16	C₁₃×#124	—	2	3	no	—
17	C₁₃×#121	—	2	6	no	—
18	C₄×D₄×C₁₃	—	2	6	no	—
19	C₂×C₄²×C₁₃	—	2	3	no	—
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×#106	—	2	6	no	—
22	C₁₃×C₄⋊C₈	—	2	6	no	—
23	C₁₃×#104	—	4	12	no	—
24	C₁₃×#102	—	2	12	no	—
25	#10300	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₁₃×#41	—	4	6	no	—
27	C₁₃×#41	—	4	6	no	—
28	C₂×Q₈×C₁₃	—	2	3	no	—
29	C₂×D₄×C₁₃	—	2	6	no	—
30	C₂×D₄×C₁₃	—	2	3	no	—
31	C₂×D₄×C₁₃	—	4	3	no	—
32	C₂²×C₄×C₁₃	—	4	1	no	—
33	C₂²×C₄×C₁₃	—	4	3	no	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
35	C₁₃×D₈	—	8	6	no	—
36	C₁₃×M₁₆	—	4	6	no	—
37	C₂×C₈×C₁₃	—	2	6	no	—
38	C₁₃×C₄⋊C₄	—	2	6	no	—
39	C₁₃×C₂²⋊C₄	—	4	6	no	—
40	C₄²×C₁₃	—	2	6	no	—
41	C₄²×C₁₃	—	4	3	no	—
42	C₄²×C₁₃	C₂×D₄	1	3	yes	—
43	C₄²×C₁₃	#41	1	1	yes	characteristic
44	#3253	C₂×C₁₃	1	3	yes	complemented
45	#1962	C₂×C₁₃	1	3	yes	complemented
46	#1309	C₂×C₁₃	1	1	yes	characteristic, complemented
47	C₂³×C₁₃	—	4	3	no	—
48	C₂³×C₁₃	#127	1	1	yes	characteristic
49	Q₈×C₁₃	—	4	6	no	—
50	D₄×C₁₃	—	4	6	no	—
51	D₄×C₁₃	—	4	6	no	—
52	D₄×C₁₃	—	4	6	no	—
53	D₄×C₁₃	—	8	6	no	—
54	C₂×C₄×C₁₃	—	2	3	no	—
55	C₂×C₄×C₁₃	—	2	3	no	—
56	C₂×C₄×C₁₃	—	4	6	no	—
57	C₂×C₄×C₁₃	—	4	3	no	—
58	C₂×C₄×C₁₃	—	8	3	no	—
59	C₂×C₄×C₁₃	—	8	3	no	—
60	C₂×C₄×C₁₃	#120	1	3	yes	—
61	C₂×C₄×C₁₃	#121	1	3	yes	—
62	C₈×C₁₃	—	4	6	no	—
63	#532	C₂²×C₁₃	1	3	yes	—
64	#476	—	2	6	no	—
65	#469	—	2	6	no	—
66	#459	—	2	6	no	—
67	#423	C₂²×C₁₃	1	3	yes	—
68	C₂×#104	—	2	6	no	—
69	C₄³	C₂²×C₁₃	1	1	yes	characteristic
70	C₂²×C₁₃	—	2	3	no	—
71	C₂²×C₁₃	—	8	3	no	—
72	C₂²×C₁₃	—	8	6	no	—
73	C₂²×C₁₃	#392	1	1	yes	characteristic
74	C₄×C₁₃	—	2	3	no	—
75	C₄×C₁₃	—	4	4	no	—
76	C₄×C₁₃	—	8	3	no	—
77	C₄×C₁₃	#453	1	3	yes	—
78	C₄×C₁₃	#454	1	3	yes	—
79	C₂×#41	—	2	3	no	—
80	C₂×D₈	—	2	6	no	—
81	C₂×M₁₆	D₄×C₁₃	1	6	yes	—
82	C₄⋊Q₈	D₄×C₁₃	1	3	yes	—
83	#127	D₄×C₁₃	1	3	yes	—
84	#124	—	2	3	no	—
85	#121	—	2	6	no	—
86	C₄×D₄	—	2	6	no	—
87	C₂×C₄²	—	2	3	no	—
88	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
89	#106	—	2	6	no	—
90	C₄⋊C₈	—	2	6	no	—
91	#104	—	4	12	no	—
92	#102	—	2	12	no	—
93	C₂×C₁₃	—	4	1	no	—
94	C₂×C₁₃	—	16	3	no	—
95	C₂×C₁₃	#2006	1	3	yes	—
96	#41	—	4	6	no	—
97	#41	—	4	6	no	—
98	C₂×Q₈	—	2	3	no	—
99	C₂×D₄	—	2	6	no	—
100	C₂×D₄	—	2	3	no	—
101	C₂×D₄	—	4	3	no	—
102	C₂²×C₄	—	4	1	no	—
103	C₂²×C₄	—	4	3	no	—
104	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
105	D₈	—	8	6	no	—
106	M₁₆	—	4	6	no	—
107	C₂×C₈	—	2	6	no	—
108	C₄⋊C₄	—	2	6	no	—
109	C₂²⋊C₄	—	4	6	no	—
110	C₄²	—	2	6	no	—
111	C₄²	—	4	3	no	—
112	C₄²	C₂×D₄×C₁₃	1	3	yes	—
113	C₄²	C₁₃×#41	1	1	yes	characteristic
114	C₁₃	#10300	1	1	yes	characteristic, direct product factor, Sylow
115	C₂³	—	4	3	no	—
116	C₂³	C₁₃×#127	1	1	yes	characteristic
117	Q₈	—	4	6	no	—
118	D₄	—	4	6	no	—
119	D₄	—	4	6	no	—
120	D₄	—	4	6	no	—
121	D₄	—	8	6	no	—
122	C₂×C₄	—	2	3	no	—
123	C₂×C₄	—	2	3	no	—
124	C₂×C₄	—	4	6	no	—
125	C₂×C₄	—	4	3	no	—
126	C₂×C₄	—	8	3	no	—
127	C₂×C₄	—	8	3	no	—
128	C₂×C₄	C₁₃×#120	1	3	yes	—
129	C₂×C₄	C₁₃×#121	1	3	yes	—
130	C₈	—	4	6	no	—
131	C₂²	—	2	3	no	—
132	C₂²	—	8	3	no	—
133	C₂²	—	8	6	no	—
134	C₂²	C₁₃×#392	1	1	yes	characteristic
135	C₄	—	2	3	no	—
136	C₄	—	4	4	no	—
137	C₄	—	8	3	no	—
138	C₄	C₁₃×#453	1	3	yes	—
139	C₄	C₁₃×#454	1	3	yes	—
140	C₂	—	4	1	no	—
141	C₂	—	16	3	no	—
142	C₂	C₁₃×#2006	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#3253

C₂

yes

maximal, complemented

C₁₃×#1962

C₂

yes

maximal, complemented

C₁₃×#1309

C₂

yes

maximal, characteristic, complemented

C₁₃×#532

C₂²

yes

—

C₁₃×#476

—

C₁₃×#469

—

C₁₃×#459

—

C₁₃×#423

C₂²

yes

—

C₂×C₁₃×#104

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₁₃×#41

—

C₂×C₁₃×D₈

—

C₂×C₁₃×M₁₆

D₄

yes

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×#127

D₄

yes

—

C₁₃×#124

—

C₁₃×#121

—

C₄×D₄×C₁₃

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₁₃×#104

—

C₁₃×#102

—

#10300

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₁₃×#41

—

C₁₃×#41

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₁₃×D₈

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

#3253

C₂×C₁₃

yes

complemented

#1962

C₂×C₁₃

yes

complemented

#1309

C₂×C₁₃

yes

characteristic, complemented

C₂³×C₁₃

—

C₂³×C₁₃

#127

yes

characteristic

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₈×C₁₃

—

#532

C₂²×C₁₃

yes

—

—

—

—

C₂²×C₁₃

yes

—

C₂×#104

—

C₄³

C₂²×C₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#453

yes

—

C₄×C₁₃

#454

yes

—

C₂×#41

—

C₂×D₈

—

C₂×M₁₆

D₄×C₁₃

yes

—

C₄⋊Q₈

D₄×C₁₃

yes

—

#127

D₄×C₁₃

yes

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

#106

—

C₄⋊C₈

—

#104

—

#102

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#2006

yes

—

#41

—

#41

—

C₂×Q₈

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

C₂×D₄×C₁₃

yes

—

105

D₈

—

106

M₁₆

—

107

C₂×C₈

—

108

C₄⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

C₂×D₄×C₁₃

yes

—

113

C₄²

C₁₃×#41

yes

characteristic

114

C₁₃

#10300

yes

characteristic, direct product factor, Sylow

115

C₂³

—

116

C₂³

C₁₃×#127

yes

characteristic

117

Q₈

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

C₁₃×#120

yes

—

129

C₂×C₄

C₁₃×#121

yes

—

130

C₈

—

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

C₁₃×#392

yes

characteristic

135

C₄

—

136

C₄

—

137

C₄

—

138

C₄

C₁₃×#453

yes

—

139

C₄

C₁₃×#454

yes

—

140

C₂

—

141

C₂

—

142

C₂

C₁₃×#2006

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#3253	C₂	semidirect
2. C₁₃×#1962	C₂	semidirect
3. C₁₃×#1309	C₂	semidirect
25. #10300	C₁₃	direct (N × H)
44. #3253	C₂×C₁₃	semidirect
45. #1962	C₂×C₁₃	semidirect
46. #1309	C₂×C₁₃	semidirect
114. C₁₃	#10300	direct (N × H)

H ≅ G/N

type

1. C₁₃×#3253

C₂

semidirect

2. C₁₃×#1962

C₂

semidirect

3. C₁₃×#1309

C₂

semidirect

25. #10300

C₁₃

direct (N × H)

44. #3253

C₂×C₁₃

semidirect

45. #1962

C₂×C₁₃

semidirect

46. #1309

C₂×C₁₃

semidirect

114. C₁₃

#10300

direct (N × H)

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

subgroup	index
C₁₃×#3253	2
C₁₃×#1962	2
C₁₃×#1309	2
#10300	13

subgroup

index

C₁₃×#3253

C₁₃×#1962

C₁₃×#1309

#10300

Subgroups — C₁₃×#10300 #15696639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10300 #15696639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10300 #15696639