Group #15828667 — subgroups

Subgroups — #15828667

Order 3328.

712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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	#13123467	C₂	1	3	yes	maximal
2	#13113139	C₂	1	3	yes	maximal, complemented
3	#13113137	C₂	1	6	yes	maximal, complemented
4	#13113135	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1455	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
7	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
8	#11718787	C₄	1	6	yes	—
9	#11718779	C₄	1	6	yes	—
10	C₄×#6099	C₂²	1	3	yes	—
11	#11718366	C₄	1	12	yes	—
12	#11718346	C₂²	1	6	yes	—
13	#11718346	C₂²	1	6	yes	—
14	C₁₃×#322	C₂²	1	3	yes	complemented
15	C₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	#11718047	C₂²	1	3	yes	complemented
17	#11718046	C₂²	1	6	yes	complemented
18	C₈×#1055	C₂²	1	3	yes	complemented
19	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	—
20	C₂×C₁₃×M₁₆	C₂×C₄	1	6	yes	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
23	C₂×#6099	C₂×C₄	1	6	yes	—
24	C₄²×D₁₃	C₂×C₄	1	6	yes	—
25	C₄²×D₁₃	C₂³	1	2	yes	—
26	C₁₃×#97	C₂×C₄	1	6	yes	—
27	C₄×C₈×C₁₃	C₂³	1	3	yes	—
28	C₄×C₈×C₁₃	C₂³	1	3	yes	—
29	#88060	C₂×C₄	1	12	yes	—
30	#88060	C₂×C₄	1	12	yes	—
31	#88054	C₂×C₄	1	12	yes	—
32	#88054	C₂×C₄	1	12	yes	—
33	#88043	C₂×C₄	1	6	yes	—
34	C₄×#1055	C₂³	1	6	yes	—
35	#17339	—	13	1	no	maximal, Sylow
36	C₂³×D₁₃	C₄²	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
38	C₂²×Dic₁₃	C₄²	1	3	yes	—
39	C₂×C₄×D₁₃	—	4	6	no	—
40	C₂×C₄×D₁₃	C₄²	1	6	yes	—
41	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
42	C₁₃×M₁₆	—	4	6	no	—
43	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
45	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
46	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₄×Dic₁₃	C₄²	1	6	yes	—
48	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
49	#6099	—	4	6	no	—
50	C₂×#1055	C₂²×C₄	1	12	yes	—
51	#2920	—	13	3	no	—
52	#1455	—	13	3	no	—
53	#1455	D₁₃	1	1	yes	characteristic, complemented
54	#1454	—	13	6	no	—
55	#1454	—	13	2	no	—
56	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₂²×D₁₃	—	4	3	no	—
58	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
59	C₂×C₄×C₁₃	—	2	6	no	—
60	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
61	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
62	C₂×Dic₁₃	—	4	3	no	—
63	C₂×Dic₁₃	C₂×C₄²	1	6	yes	—
64	C₄×D₁₃	—	2	12	no	—
65	C₄×D₁₃	—	4	6	no	—
66	C₈×C₁₃	—	2	6	no	—
67	C₈×C₁₃	—	2	6	no	—
68	#1055	—	2	12	no	—
69	C₂²×C₄²	—	13	1	no	—
70	#432	—	13	12	no	—
71	#431	—	13	6	no	—
72	#431	—	13	6	no	—
73	#423	—	13	6	no	—
74	#407	—	13	6	no	—
75	C₄×M₁₆	—	13	3	no	—
76	C₄×M₁₆	C₂×D₁₃	1	3	yes	—
77	#322	—	13	6	no	—
78	#322	—	13	3	no	—
79	#322	C₂×D₁₃	1	3	yes	complemented
80	C₈²	—	13	3	no	—
81	C₈²	C₂×D₁₃	1	1	yes	characteristic, complemented
82	C₂²×C₁₃	—	2	3	no	—
83	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
84	C₂×D₁₃	—	2	6	no	—
85	C₂×D₁₃	—	4	4	no	—
86	C₄×C₁₃	—	2	3	no	—
87	C₄×C₁₃	#568	1	6	yes	—
88	Dic₁₃	—	2	6	no	—
89	C₂³×C₄	—	13	3	no	—
90	C₂×M₁₆	—	13	6	no	—
91	C₂×M₁₆	C₄×D₁₃	1	6	yes	—
92	C₂×C₄²	—	13	3	no	—
93	C₂×C₄²	—	13	6	no	—
94	C₂×C₄²	—	13	2	no	—
95	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
96	C₄⋊C₈	—	13	12	no	—
97	C₄⋊C₈	—	13	12	no	—
98	C₂²⋊C₈	—	13	12	no	—
99	C₂²⋊C₈	—	13	12	no	—
100	#97	—	13	6	no	—
101	#97	C₄×D₁₃	1	6	yes	—
102	C₄×C₈	—	13	6	no	—
103	C₄×C₈	C₂²×D₁₃	1	3	yes	—
104	C₄×C₈	C₂²×D₁₃	1	3	yes	—
105	C₂×C₁₃	—	4	1	no	—
106	C₂×C₁₃	#2873	1	3	yes	—
107	D₁₃	—	4	2	no	—
108	C₂⁴	—	13	1	no	—
109	C₂²×C₄	—	13	3	no	—
110	C₂²×C₄	—	13	6	no	—
111	C₂²×C₄	—	13	6	no	—
112	C₂²×C₄	—	52	6	no	—
113	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
114	M₁₆	—	4	6	no	—
115	M₁₆	—	52	6	no	—
116	C₂×C₈	—	13	12	no	—
117	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
118	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
119	C₄²	—	13	6	no	—
120	C₄²	—	13	6	no	—
121	C₄²	C₂×C₄×D₁₃	1	3	yes	—
122	C₄²	C₂³×D₁₃	1	1	yes	characteristic
123	C₁₃	#17339	1	1	yes	characteristic, complemented, Sylow
124	C₂³	—	13	2	no	—
125	C₂³	—	52	3	no	—
126	C₂³	C₄²×D₁₃	1	1	yes	characteristic
127	C₂×C₄	—	2	6	no	—
128	C₂×C₄	—	13	6	no	—
129	C₂×C₄	—	26	12	no	—
130	C₂×C₄	—	52	6	no	—
131	C₂×C₄	—	52	3	no	—
132	C₂×C₄	C₄²×D₁₃	1	3	yes	—
133	C₂×C₄	C₂²×C₄×D₁₃	1	3	yes	—
134	C₈	—	2	6	no	—
135	C₈	—	2	6	no	—
136	C₈	—	26	12	no	—
137	C₂²	—	2	3	no	—
138	C₂²	—	26	6	no	—
139	C₂²	—	52	4	no	—
140	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
141	C₄	—	2	3	no	—
142	C₄	—	26	6	no	—
143	C₄	#11719450	1	6	yes	—
144	C₂	—	4	1	no	—
145	C₂	—	52	2	no	—
146	C₂	#13123253	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13123467

C₂

yes

maximal

#13113139

C₂

yes

maximal, complemented

#13113137

C₂

yes

maximal, complemented

#13113135

C₂

yes

maximal, complemented

C₁₃×#1455

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₁₃

C₂²

yes

characteristic

C₄×C₁₃×M₁₆

C₂²

yes

—

#11718787

C₄

yes

—

#11718779

C₄

yes

—

C₄×#6099

C₂²

yes

—

#11718366

C₄

yes

—

#11718346

C₂²

yes

—

#11718346

C₂²

yes

—

C₁₃×#322

C₂²

yes

complemented

C₈²×C₁₃

C₂²

yes

characteristic, complemented

#11718047

C₂²

yes

complemented

#11718046

C₂²

yes

complemented

C₈×#1055

C₂²

yes

complemented

C₂²×C₄×D₁₃

C₂×C₄

yes

—

C₂×C₁₃×M₁₆

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×#6099

C₂×C₄

yes

—

C₄²×D₁₃

C₂×C₄

yes

—

C₄²×D₁₃

C₂³

yes

—

C₁₃×#97

C₂×C₄

yes

—

C₄×C₈×C₁₃

C₂³

yes

—

C₄×C₈×C₁₃

C₂³

yes

—

#88060

C₂×C₄

yes

—

#88060

C₂×C₄

yes

—

#88054

C₂×C₄

yes

—

#88054

C₂×C₄

yes

—

#88043

C₂×C₄

yes

—

C₄×#1055

C₂³

yes

—

#17339

—

maximal, Sylow

C₂³×D₁₃

C₄²

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₄²

yes

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₄²

yes

—

C₂×C₄×D₁₃

C₂²×C₄

yes

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

C₂⁴

yes

characteristic

C₄×Dic₁₃

C₄²

yes

—

C₄×Dic₁₃

C₂²×C₄

yes

—

#6099

—

C₂×#1055

C₂²×C₄

yes

—

#2920

—

#1455

—

#1455

D₁₃

yes

characteristic, complemented

#1454

—

#1454

—

C₂³×C₁₃

C₂×C₄²

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

C₂×C₄²

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄²

yes

—

C₂×C₄×C₁₃

C₂³×C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₄²

yes

—

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

C₂²×C₄²

—

—

—

—

—

—

C₄×M₁₆

—

C₄×M₁₆

C₂×D₁₃

yes

—

#322

—

#322

—

#322

C₂×D₁₃

yes

complemented

C₈²

—

C₈²

C₂×D₁₃

yes

characteristic, complemented

C₂²×C₁₃

—

C₂²×C₁₃

C₂²×C₄²

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#568

yes

—

Dic₁₃

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

100

#97

—

101

#97

C₄×D₁₃

yes

—

102

C₄×C₈

—

103

C₄×C₈

C₂²×D₁₃

yes

—

104

C₄×C₈

C₂²×D₁₃

yes

—

105

C₂×C₁₃

—

106

C₂×C₁₃

#2873

yes

—

107

D₁₃

—

108

C₂⁴

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

C₂×C₄×D₁₃

yes

—

114

M₁₆

—

115

M₁₆

—

116

C₂×C₈

—

117

C₂×C₈

C₂×C₄×D₁₃

yes

—

118

C₂×C₈

C₂×C₄×D₁₃

yes

—

119

C₄²

—

120

C₄²

—

121

C₄²

C₂×C₄×D₁₃

yes

—

122

C₄²

C₂³×D₁₃

yes

characteristic

123

C₁₃

#17339

yes

characteristic, complemented, Sylow

124

C₂³

—

125

C₂³

—

126

C₂³

C₄²×D₁₃

yes

characteristic

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

C₄²×D₁₃

yes

—

133

C₂×C₄

C₂²×C₄×D₁₃

yes

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

C₂×C₄²×D₁₃

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

#11719450

yes

—

144

C₂

—

145

C₂

—

146

C₂

#13123253

yes

—

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#1455	C₂
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1455	D₁₃
hypocenter	C₁₃	#17339
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #1455

subgroup

G/H

center, Frattini

C₄²

C₂³×D₁₃

commutator, socle

C₂²×C₁₃

C₂²×C₄²

Fitting

C₁₃×#1455

C₂

prime radical

C₂³×D₁₃

C₄²

cosocle

C₄²×C₁₃

C₂⁴

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₄² ◁ #1455

N	H ≅ G/N	type
2. #13113139	C₂	semidirect
3. #13113137	C₂	semidirect
4. #13113135	C₂	semidirect
5. C₁₃×#1455	C₂	semidirect
14. C₁₃×#322	C₂²	semidirect
15. C₈²×C₁₃	C₂²	semidirect
16. #11718047	C₂²	semidirect
17. #11718046	C₂²	semidirect
18. C₈×#1055	C₂²	semidirect
53. #1455	D₁₃	semidirect
79. #322	C₂×D₁₃	semidirect
81. C₈²	C₂×D₁₃	semidirect
123. C₁₃	#17339	semidirect

H ≅ G/N

type

2. #13113139

C₂

semidirect

3. #13113137

C₂

semidirect

4. #13113135

C₂

semidirect

5. C₁₃×#1455

C₂

semidirect

14. C₁₃×#322

C₂²

semidirect

15. C₈²×C₁₃

C₂²

semidirect

16. #11718047

C₂²

semidirect

17. #11718046

C₂²

semidirect

18. C₈×#1055

C₂²

semidirect

53. #1455

D₁₃

semidirect

79. #322

C₂×D₁₃

semidirect

81. C₈²

C₂×D₁₃

semidirect

123. C₁₃

#17339

semidirect

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

subgroup	index
#13123467	2
#13113139	2
#13113137	2
#13113135	2
C₁₃×#1455	2
#17339	13

subgroup

index

C₁₃×#1455

Subgroups — #15828667

Conjugacy classes of subgroups

Complements

Maximal subgroups