Group #15794270 — subgroups

Subgroups — #15794270

Order 3328.

1422 conjugacy classes of subgroups; only the 411 normal subgroups are shown.

normal subgroups only

This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 411 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×#11718598	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13113067	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×#6101	C₂²	1	4	yes	—
7	C₂²×C₄×Dic₁₃	C₂²	1	6	yes	—
8	C₁₃×#383	—	2	4	no	—
9	C₂×C₁₃×#95	C₂²	1	6	yes	—
10	C₂×#88071	C₂²	1	12	yes	—
11	C₂×#88071	C₂²	1	6	yes	—
12	#11718598	C₄	1	8	yes	complemented
13	C₄²×Dic₁₃	—	2	4	no	—
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×#6101	—	2	24	no	—
22	C₂×C₄×Dic₁₃	—	2	12	no	—
23	C₂×C₄×Dic₁₃	—	2	24	no	—
24	C₁₃×#95	—	2	12	no	—
25	#88071	—	2	24	no	—
26	#88071	C₂×C₄	1	24	yes	—
27	#14710	—	13	1	no	maximal, Sylow
28	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	—	2	12	no	—
30	C₂²×C₄×C₁₃	—	2	4	no	—
31	C₂²×C₄×C₁₃	—	2	12	no	—
32	C₂²×C₄×C₁₃	—	2	12	no	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
35	C₂²×C₄×C₁₃	C₂×Q₈	1	6	yes	—
36	C₂²×Dic₁₃	—	2	4	no	—
37	C₂²×Dic₁₃	—	2	12	no	—
38	C₂²×Dic₁₃	—	2	12	no	—
39	C₂²×Dic₁₃	—	2	12	no	—
40	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
41	C₂²×Dic₁₃	#41	1	24	yes	—
42	C₄²×C₁₃	C₄⋊C₄	1	16	yes	complemented
43	#6101	—	4	16	no	—
44	C₄×Dic₁₃	—	2	48	no	—
45	C₂×#383	—	13	1	no	—
46	C₂×#383	D₁₃	1	1	yes	characteristic
47	C₂×C₄³	—	13	1	no	—
48	#1436	—	13	12	no	—
49	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
50	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
51	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
52	C₂³×C₁₃	C₂×#41	1	12	yes	—
53	C₂×C₄×C₁₃	—	2	12	no	—
54	C₂×C₄×C₁₃	—	2	12	no	—
55	C₂×C₄×C₁₃	—	2	12	no	—
56	C₂×C₄×C₁₃	—	4	12	no	—
57	C₂×C₄×C₁₃	—	4	4	no	—
58	C₂×C₄×C₁₃	—	4	12	no	—
59	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
60	C₂×Dic₁₃	—	2	24	no	—
61	C₂×Dic₁₃	—	2	24	no	—
62	C₂×Dic₁₃	—	2	24	no	—
63	C₂×Dic₁₃	—	4	4	no	—
64	C₂×Dic₁₃	—	4	12	no	—
65	C₂×Dic₁₃	#126	1	16	yes	—
66	C₂²×C₄⋊C₄	—	13	4	no	—
67	C₂²×C₄²	—	13	6	no	—
68	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
69	#383	—	2	4	no	—
70	#383	—	13	8	no	—
71	C₂×#95	—	13	6	no	—
72	C₂×#95	—	13	12	no	—
73	C₂×#95	C₂×D₁₃	1	6	yes	—
74	C₄³	—	26	4	no	—
75	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₁₃	C₄×#41	1	6	yes	—
77	C₂²×C₁₃	#525	1	6	yes	—
78	C₂²×C₁₃	C₂×#126	1	4	yes	—
79	C₂²×C₁₃	#529	1	12	yes	—
80	C₂²×C₁₃	#533	1	6	yes	—
81	C₄×C₁₃	—	2	12	no	—
82	C₄×C₁₃	—	8	4	no	—
83	Dic₁₃	—	2	16	no	—
84	Dic₁₃	—	4	8	no	—
85	C₂³×C₄	—	13	4	no	—
86	C₂³×C₄	—	13	4	no	—
87	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
88	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
89	C₂×C₄⋊C₄	—	26	24	no	—
90	C₂×C₄²	—	26	24	no	—
91	C₂×C₄²	—	26	12	no	—
92	C₂×C₄²	Dic₂₆	1	4	yes	—
93	C₂×C₄²	C₄×D₁₃	1	4	yes	—
94	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
95	#95	—	2	12	no	—
96	#95	—	13	24	no	—
97	#95	—	26	24	no	—
98	C₂×C₁₃	#2296	1	3	yes	—
99	C₂×C₁₃	C₄×#126	1	4	yes	—
100	C₂×C₁₃	#2852	1	4	yes	—
101	C₂×C₁₃	#2863	1	4	yes	—
102	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
103	C₂²×C₄	—	2	12	no	—
104	C₂²×C₄	—	2	12	no	—
105	C₂²×C₄	—	2	12	no	—
106	C₂²×C₄	—	2	4	no	—
107	C₂²×C₄	—	13	24	no	—
108	C₂²×C₄	—	13	8	no	—
109	C₂²×C₄	—	26	12	no	—
110	C₂²×C₄	—	26	4	no	—
111	C₂²×C₄	—	26	12	no	—
112	C₂²×C₄	—	26	12	no	—
113	C₂²×C₄	C₂×Dic₂₆	1	6	yes	—
114	C₂²×C₄	C₂×C₄×D₁₃	1	6	yes	—
115	C₂²×C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
116	C₄⋊C₄	—	52	16	no	—
117	C₄²	—	26	48	no	—
118	C₄²	#6101	1	16	yes	complemented
119	C₁₃	#14710	1	1	yes	characteristic, complemented, Sylow
120	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
121	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
122	C₂³	#41×D₁₃	1	12	yes	—
123	C₂³	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
124	C₂×C₄	—	2	12	no	—
125	C₂×C₄	—	2	12	no	—
126	C₂×C₄	—	2	12	no	—
127	C₂×C₄	—	4	12	no	—
128	C₂×C₄	—	4	4	no	—
129	C₂×C₄	—	4	12	no	—
130	C₂×C₄	—	13	16	no	—
131	C₂×C₄	—	26	24	no	—
132	C₂×C₄	—	26	24	no	—
133	C₂×C₄	—	26	24	no	—
134	C₂×C₄	—	52	4	no	—
135	C₂×C₄	—	52	12	no	—
136	C₂×C₄	C₂×#6101	1	12	yes	—
137	C₂²	#11719222	1	6	yes	—
138	C₂²	#11719227	1	6	yes	—
139	C₂²	D₁₃×#126	1	4	yes	—
140	C₂²	#11719411	1	12	yes	—
141	C₂²	C₂²×#6101	1	1	yes	characteristic
142	C₂²	#11719533	1	6	yes	—
143	C₄	—	2	12	no	—
144	C₄	—	8	4	no	—
145	C₄	—	26	16	no	—
146	C₄	—	52	8	no	—
147	C₂	#13117318	1	3	yes	—
148	C₂	#13117384	1	4	yes	—
149	C₂	#13123148	1	4	yes	—
150	C₂	#13123216	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718598

C₂

yes

maximal, characteristic

C₂×C₄²×Dic₁₃

C₂

yes

maximal, characteristic

#13113067

C₂

yes

maximal

C₂×C₁₃×#383

C₂

yes

maximal, characteristic

C₂²×C₄²×C₁₃

C₂²

yes

characteristic

C₂²×#6101

C₂²

yes

—

C₂²×C₄×Dic₁₃

C₂²

yes

—

C₁₃×#383

—

C₂×C₁₃×#95

C₂²

yes

—

C₂×#88071

C₂²

yes

—

C₂×#88071

C₂²

yes

—

#11718598

C₄

yes

complemented

C₄²×Dic₁₃

—

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×#6101

—

C₂×C₄×Dic₁₃

—

C₂×C₄×Dic₁₃

—

C₁₃×#95

—

#88071

—

#88071

C₂×C₄

yes

—

#14710

—

maximal, Sylow

C₂⁴×C₁₃

C₂⁴

yes

characteristic

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×C₄

yes

—

C₂²×Dic₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

complemented

#6101

—

C₄×Dic₁₃

—

C₂×#383

—

C₂×#383

D₁₃

yes

characteristic

C₂×C₄³

—

#1436

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂³×C₁₃

C₂²×D₄

yes

characteristic

C₂³×C₁₃

C₂²×Q₈

yes

characteristic

C₂³×C₁₃

C₂×#41

yes

—

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

#126

yes

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

—

C₂²×C₄²

C₂×D₁₃

yes

characteristic

#383

—

#383

—

C₂×#95

—

C₂×#95

—

C₂×#95

C₂×D₁₃

yes

—

C₄³

—

C₂²×C₁₃

C₂²×C₄⋊C₄

yes

characteristic

C₂²×C₁₃

C₄×#41

yes

—

C₂²×C₁₃

#525

yes

—

C₂²×C₁₃

C₂×#126

yes

—

C₂²×C₁₃

#529

yes

—

C₂²×C₁₃

#533

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×C₄²

—

C₂×C₄²

—

C₂×C₄²

Dic₂₆

yes

—

C₂×C₄²

C₄×D₁₃

yes

—

C₂×C₄²

C₂²⋊D₁₃

yes

—

#95

—

#95

—

#95

—

C₂×C₁₃

#2296

yes

—

C₂×C₁₃

C₄×#126

yes

—

100

C₂×C₁₃

#2852

yes

—

101

C₂×C₁₃

#2863

yes

—

102

C₂⁴

C₂³×D₁₃

yes

characteristic

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂²×C₄

—

106

C₂²×C₄

—

107

C₂²×C₄

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×Dic₂₆

yes

—

114

C₂²×C₄

C₂×C₄×D₁₃

yes

—

115

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

116

C₄⋊C₄

—

117

C₄²

—

118

C₄²

#6101

yes

complemented

119

C₁₃

#14710

yes

characteristic, complemented, Sylow

120

C₂³

C₂²×Dic₂₆

yes

characteristic

121

C₂³

C₂²×C₄×D₁₃

yes

characteristic

122

C₂³

#41×D₁₃

yes

—

123

C₂³

C₂²×C₂²⋊D₁₃

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

C₂×#6101

yes

—

137

C₂²

#11719222

yes

—

138

C₂²

#11719227

yes

—

139

C₂²

D₁₃×#126

yes

—

140

C₂²

#11719411

yes

—

141

C₂²

C₂²×#6101

yes

characteristic

142

C₂²

#11719533

yes

—

143

C₄

—

144

C₄

—

145

C₄

—

146

C₄

—

147

C₂

#13117318

yes

—

148

C₂

#13117384

yes

—

149

C₂

#13123148

yes

—

150

C₂

#13123216

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	#14710
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
12. #11718598	C₄	semidirect
42. C₄²×C₁₃	C₄⋊C₄	semidirect
118. C₄²	#6101	semidirect
119. C₁₃	#14710	semidirect

H ≅ G/N

type

12. #11718598

C₄

semidirect

42. C₄²×C₁₃

C₄⋊C₄

semidirect

118. C₄²

#6101

semidirect

119. C₁₃

#14710

semidirect

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

subgroup	index
C₂×#11718598	2
C₂×C₄²×Dic₁₃	2
#13113067	2
C₂×C₁₃×#383	2
#14710	13

subgroup

index

C₂×#11718598

C₂×C₄²×Dic₁₃

#13113067

C₂×C₁₃×#383

#14710

Subgroups — #15794270

Conjugacy classes of subgroups

Complements

Maximal subgroups