Group #15794062 — subgroups

Subgroups — #15794062

Order 3328.

1182 conjugacy classes of subgroups; only the 371 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 371 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×#11718596	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718598	C₂	1	1	yes	maximal, characteristic
3	#13113088	C₂	1	12	yes	maximal
4	C₂×C₁₃×#383	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊Dic₁₃	C₂²	1	6	yes	—
7	C₂²×#6101	C₂²	1	4	yes	—
8	C₁₃×#383	—	2	4	no	—
9	C₂×C₁₃×#95	C₂²	1	6	yes	—
10	C₂×#88071	C₂²	1	6	yes	—
11	C₂×#88071	C₂²	1	12	yes	—
12	#11718598	—	2	4	no	—
13	#11718596	C₄	1	8	yes	complemented
14	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
16	C₂³×Dic₁₃	C₂³	1	4	yes	—
17	C₂³×Dic₁₃	C₂³	1	4	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₃	D₄	1	4	yes	—
20	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
21	C₂×C₄⋊Dic₁₃	—	4	6	no	—
22	C₂×C₄⋊Dic₁₃	—	4	6	no	—
23	C₂×C₄⋊Dic₁₃	C₂×C₄	1	24	yes	—
24	C₂×#6101	—	4	12	no	—
25	C₁₃×#95	—	2	12	no	—
26	#88071	—	2	12	no	—
27	#88071	—	4	12	no	—
28	#14676	—	13	1	no	maximal, Sylow
29	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	—	2	6	no	—
31	C₂²×C₄×C₁₃	—	2	6	no	—
32	C₂²×C₄×C₁₃	—	2	4	no	—
33	C₂²×C₄×C₁₃	—	2	12	no	—
34	C₂²×C₄×C₁₃	—	2	12	no	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
36	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
37	C₂²×C₄×C₁₃	C₂×Q₈	1	6	yes	—
38	C₂²×Dic₁₃	—	2	12	no	—
39	C₂²×Dic₁₃	—	2	12	no	—
40	C₂²×Dic₁₃	—	2	4	no	—
41	C₂²×Dic₁₃	—	2	12	no	—
42	C₂²×Dic₁₃	—	2	12	no	—
43	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
44	C₄²×C₁₃	C₄⋊C₄	1	16	yes	complemented
45	C₄⋊Dic₁₃	—	4	24	no	—
46	#6101	—	4	16	no	—
47	C₂×#384	—	13	1	no	—
48	C₂×#383	—	13	1	no	—
49	C₂×#383	D₁₃	1	1	yes	characteristic
50	#1441	—	13	12	no	—
51	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
52	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
53	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
54	C₂³×C₁₃	H(5,𝔽₂)	1	6	yes	—
55	C₂³×C₁₃	2₋¹⁺⁴	1	6	yes	—
56	C₂×C₄×C₁₃	—	2	6	no	—
57	C₂×C₄×C₁₃	—	2	6	no	—
58	C₂×C₄×C₁₃	—	2	12	no	—
59	C₂×C₄×C₁₃	—	2	12	no	—
60	C₂×C₄×C₁₃	—	4	12	no	—
61	C₂×C₄×C₁₃	—	4	4	no	—
62	C₂×C₄×C₁₃	—	4	12	no	—
63	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
64	C₂×Dic₁₃	—	2	24	no	—
65	C₂×Dic₁₃	—	4	4	no	—
66	C₂×Dic₁₃	—	4	12	no	—
67	C₂×Dic₁₃	—	4	12	no	—
68	C₂×Dic₁₃	—	4	4	no	—
69	C₂×Dic₁₃	—	4	12	no	—
70	C₂²×C₄⋊C₄	—	13	6	no	—
71	C₂²×C₄⋊C₄	—	13	4	no	—
72	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
73	#384	—	13	8	no	—
74	#383	—	2	4	no	—
75	#383	—	26	4	no	—
76	C₂×#95	—	13	6	no	—
77	C₂×#95	—	13	12	no	—
78	C₂×#95	C₂×D₁₃	1	6	yes	—
79	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₁₃	#518	1	3	yes	—
81	C₂²×C₁₃	#519	1	3	yes	—
82	C₂²×C₁₃	#537	1	6	yes	—
83	C₂²×C₁₃	#544	1	6	yes	—
84	C₂²×C₁₃	#560	1	4	yes	—
85	C₂²×C₁₃	#563	1	12	yes	—
86	C₄×C₁₃	—	2	12	no	—
87	C₄×C₁₃	—	8	4	no	—
88	Dic₁₃	—	4	8	no	—
89	Dic₁₃	—	8	4	no	—
90	C₂³×C₄	—	13	4	no	—
91	C₂³×C₄	—	13	4	no	—
92	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
93	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
94	C₂×C₄⋊C₄	—	13	24	no	—
95	C₂×C₄⋊C₄	—	52	12	no	—
96	C₂×C₄⋊C₄	—	52	6	no	—
97	C₂×C₄⋊C₄	—	52	6	no	—
98	C₂×C₄²	Dic₂₆	1	4	yes	—
99	C₂×C₄²	C₄×D₁₃	1	4	yes	—
100	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
101	#95	—	2	12	no	—
102	#95	—	26	12	no	—
103	#95	—	52	12	no	—
104	C₂×C₁₃	#2316	1	3	yes	—
105	C₂×C₁₃	#2380	1	1	yes	characteristic
106	C₂×C₁₃	#2381	1	3	yes	—
107	C₂×C₁₃	#2823	1	4	yes	—
108	C₂×C₁₃	#2843	1	4	yes	—
109	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
110	C₂²×C₄	—	2	6	no	—
111	C₂²×C₄	—	2	6	no	—
112	C₂²×C₄	—	2	12	no	—
113	C₂²×C₄	—	2	12	no	—
114	C₂²×C₄	—	2	4	no	—
115	C₂²×C₄	—	13	8	no	—
116	C₂²×C₄	—	26	12	no	—
117	C₂²×C₄	—	26	12	no	—
118	C₂²×C₄	—	26	12	no	—
119	C₂²×C₄	—	26	12	no	—
120	C₂²×C₄	—	26	4	no	—
121	C₂²×C₄	C₂×Dic₂₆	1	6	yes	—
122	C₂²×C₄	C₂×C₄×D₁₃	1	6	yes	—
123	C₂²×C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
124	C₄⋊C₄	—	52	24	no	—
125	C₄⋊C₄	—	52	16	no	—
126	C₄²	#6101	1	16	yes	complemented
127	C₁₃	#14676	1	1	yes	characteristic, complemented, Sylow
128	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
129	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
130	C₂³	#88256	1	6	yes	—
131	C₂³	#88257	1	6	yes	—
132	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
133	C₂×C₄	—	2	6	no	—
134	C₂×C₄	—	2	12	no	—
135	C₂×C₄	—	2	6	no	—
136	C₂×C₄	—	2	12	no	—
137	C₂×C₄	—	4	12	no	—
138	C₂×C₄	—	4	4	no	—
139	C₂×C₄	—	4	12	no	—
140	C₂×C₄	—	26	24	no	—
141	C₂×C₄	—	52	4	no	—
142	C₂×C₄	—	52	12	no	—
143	C₂×C₄	—	52	12	no	—
144	C₂×C₄	—	52	4	no	—
145	C₂×C₄	—	52	12	no	—
146	C₂×C₄	C₂×#6101	1	12	yes	—
147	C₂²	#11719221	1	3	yes	—
148	C₂²	#11719224	1	6	yes	—
149	C₂²	#11719226	1	3	yes	—
150	C₂²	#11719416	1	4	yes	—
151	C₂²	#11719417	1	12	yes	—
152	C₂²	C₂²×#6101	1	1	yes	characteristic
153	C₂²	#11719538	1	6	yes	—
154	C₄	—	2	12	no	—
155	C₄	—	8	4	no	—
156	C₄	—	52	8	no	—
157	C₄	—	104	4	no	—
158	C₂	#13117452	1	3	yes	—
159	C₂	#13118012	1	1	yes	characteristic
160	C₂	#13118016	1	3	yes	—
161	C₂	#13122908	1	4	yes	—
162	C₂	#13123103	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718596

C₂

yes

maximal, characteristic

C₂×#11718598

C₂

yes

maximal, characteristic

#13113088

C₂

yes

maximal

C₂×C₁₃×#383

C₂

yes

maximal, characteristic

C₂²×C₄²×C₁₃

C₂²

yes

characteristic

C₂²×C₄⋊Dic₁₃

C₂²

yes

—

C₂²×#6101

C₂²

yes

—

C₁₃×#383

—

C₂×C₁₃×#95

C₂²

yes

—

C₂×#88071

C₂²

yes

—

C₂×#88071

C₂²

yes

—

#11718598

—

#11718596

C₄

yes

complemented

C₂³×C₄×C₁₃

C₂³

yes

—

C₂³×C₄×C₁₃

C₂³

yes

—

C₂³×Dic₁₃

C₂³

yes

—

C₂³×Dic₁₃

C₂³

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

Q₈

yes

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

C₂×C₄

yes

—

C₂×#6101

—

C₁₃×#95

—

—

—

—

C₂⁴×C₁₃

C₂⁴

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×Q₈

yes

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

complemented

C₄⋊Dic₁₃

—

—

—

—

D₁₃

yes

characteristic

#1441

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂³×C₁₃

C₂²×D₄

yes

characteristic

C₂³×C₁₃

C₂²×Q₈

yes

characteristic

C₂³×C₁₃

H(5,𝔽₂)

yes

—

C₂³×C₁₃

2₋¹⁺⁴

yes

—

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⋊C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

C₂×D₁₃

yes

—

—

—

C₂×#95

—

C₂×#95

—

C₂×#95

C₂×D₁₃

yes

—

C₂²×C₁₃

C₂²×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

#518

yes

—

C₂²×C₁₃

#519

yes

—

C₂²×C₁₃

#537

yes

—

C₂²×C₁₃

#544

yes

—

C₂²×C₁₃

#560

yes

—

C₂²×C₁₃

#563

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂²×D₁₃

yes

—

C₂³×C₄

C₂²×D₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

Dic₂₆

yes

—

C₂×C₄²

C₄×D₁₃

yes

—

100

C₂×C₄²

C₂²⋊D₁₃

yes

—

101

#95

—

102

#95

—

103

#95

—

104

C₂×C₁₃

#2316

yes

—

105

C₂×C₁₃

#2380

yes

characteristic

106

C₂×C₁₃

#2381

yes

—

107

C₂×C₁₃

#2823

yes

—

108

C₂×C₁₃

#2843

yes

—

109

C₂⁴

C₂³×D₁₃

yes

characteristic

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

114

C₂²×C₄

—

115

C₂²×C₄

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

C₂×Dic₂₆

yes

—

122

C₂²×C₄

C₂×C₄×D₁₃

yes

—

123

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄²

#6101

yes

complemented

127

C₁₃

#14676

yes

characteristic, complemented, Sylow

128

C₂³

C₂²×Dic₂₆

yes

characteristic

129

C₂³

C₂²×C₄×D₁₃

yes

characteristic

130

C₂³

#88256

yes

—

131

C₂³

#88257

yes

—

132

C₂³

C₂²×C₂²⋊D₁₃

yes

characteristic

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

—

139

C₂×C₄

—

140

C₂×C₄

—

141

C₂×C₄

—

142

C₂×C₄

—

143

C₂×C₄

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

C₂×#6101

yes

—

147

C₂²

#11719221

yes

—

148

C₂²

#11719224

yes

—

149

C₂²

#11719226

yes

—

150

C₂²

#11719416

yes

—

151

C₂²

#11719417

yes

—

152

C₂²

C₂²×#6101

yes

characteristic

153

C₂²

#11719538

yes

—

154

C₄

—

155

C₄

—

156

C₄

—

157

C₄

—

104

—

158

C₂

#13117452

yes

—

159

C₂

#13118012

yes

characteristic

160

C₂

#13118016

yes

—

161

C₂

#13122908

yes

—

162

C₂

#13123103

yes

—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₃
commutator	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₁₃×#383	C₂
socle, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×#383	D₁₃
hypocenter	C₁₃	#14676
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#383

subgroup

G/H

center, Frattini

C₂⁴

C₂³×D₁₃

commutator

C₂³×C₁₃

C₂³×C₄

Fitting

C₂×C₁₃×#383

C₂

socle, prime radical, cosocle

C₂⁴×C₁₃

C₂⁴

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂⁴ ◁ C₂×#383

N	H ≅ G/N	type
13. #11718596	C₄	semidirect
44. C₄²×C₁₃	C₄⋊C₄	semidirect
126. C₄²	#6101	semidirect
127. C₁₃	#14676	semidirect

H ≅ G/N

type

13. #11718596

C₄

semidirect

44. C₄²×C₁₃

C₄⋊C₄

semidirect

126. C₄²

#6101

semidirect

127. C₁₃

#14676

semidirect

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

subgroup	index
C₂×#11718596	2
C₂×#11718598	2
#13113088	2
C₂×C₁₃×#383	2
#14676	13

subgroup

index

C₂×C₁₃×#383

Subgroups — #15794062

Conjugacy classes of subgroups

Complements

Maximal subgroups