Group #13130774 — subgroups

Subgroups — #13130774

Order 1664.

256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 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×#88102	C₂	1	2	yes	maximal
2	C₂×#88101	C₂	1	2	yes	maximal
3	#11719060	C₂	1	1	yes	maximal, characteristic
4	#11719059	C₂	1	1	yes	maximal, characteristic
5	D₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#261	—	2	2	no	—
7	C₂×C₄⋊#261	C₂²	1	2	yes	—
8	C₂×C₄⋊#261	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊#261	C₂²	1	1	yes	characteristic
10	C₂×C₈×D₁₃	C₂²	1	2	yes	—
11	C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	(C₂×#261)⋊C₄	—	2	2	no	—
13	#88102	—	2	4	no	—
14	#88101	—	2	4	no	—
15	C₁₃×#97	C₄	1	1	yes	characteristic, complemented
16	#88055	C₄	1	2	yes	complemented
17	#88043	C₄	1	1	yes	characteristic, complemented
18	C₂²×#261	—	2	1	no	—
19	C₂²×#261	—	2	1	no	—
20	C₂²×#261	—	2	2	no	—
21	C₂×C₄×D₁₃	D₄	1	2	yes	—
22	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
23	C₄⋊#261	—	2	2	no	—
24	C₄⋊#261	—	2	2	no	—
25	C₄⋊#261	—	2	2	no	—
26	C₄⋊#261	—	2	2	no	—
27	C₄⋊#261	—	4	4	no	—
28	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₃	Q₈	1	2	yes	—
32	C₂×#1055	C₂×C₄	1	2	yes	—
33	C₈×D₁₃	D₄	1	4	yes	—
34	C₈×D₁₃	Q₈	1	4	yes	—
35	#1847	—	13	1	no	maximal, Sylow
36	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
37	C₂×#261	—	4	2	no	—
38	C₂×#261	—	4	1	no	—
39	C₂×#261	—	4	1	no	—
40	C₂×#261	—	4	4	no	—
41	C₂×#261	—	4	2	no	—
42	C₂×#261	—	4	2	no	—
43	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
46	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₄×D₁₃	—	2	2	no	—
48	C₄×D₁₃	—	2	2	no	—
49	C₄×D₁₃	C₂×D₄	1	2	yes	—
50	C₄×D₁₃	C₂×Q₈	1	2	yes	—
51	C₈×C₁₃	C₄⋊C₄	1	4	yes	complemented
52	#1055	C₄⋊C₄	1	4	yes	complemented
53	C₂×#107	—	13	2	no	—
54	C₂×#106	—	13	2	no	—
55	C₂×#97	—	13	1	no	—
56	#384	—	13	1	no	—
57	#382	—	13	1	no	—
58	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
59	C₂×D₁₃	#127	1	1	yes	characteristic
60	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
61	C₂×D₁₃	AGL(1,ℤ/8)	1	2	yes	—
62	C₂×D₁₃	#137	1	2	yes	—
63	#261	—	8	2	no	—
64	#261	—	8	1	no	—
65	#261	—	8	1	no	—
66	C₄×C₁₃	—	2	2	no	—
67	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
68	Dic₁₃	—	2	2	no	—
69	Dic₁₃	C₄⋊Q₈	1	2	yes	—
70	C₂²×C₈	—	13	2	no	—
71	C₂×C₄⋊C₄	—	13	1	no	—
72	C₂×C₄⋊C₄	—	13	1	no	—
73	C₂×C₄⋊C₄	—	13	2	no	—
74	C₂×C₄⋊C₄	—	26	2	no	—
75	C₂×C₄²	—	13	1	no	—
76	#107	—	26	4	no	—
77	#106	—	26	4	no	—
78	#97	—	13	2	no	—
79	#97	—	13	1	no	—
80	#97	#261	1	1	yes	characteristic, complemented
81	#95	—	26	2	no	—
82	C₂×C₁₃	#384	1	1	yes	characteristic
83	C₂×C₁₃	#428	1	2	yes	—
84	D₁₃	#496	1	1	yes	characteristic
85	D₁₃	#497	1	1	yes	characteristic
86	D₁₃	#501	1	2	yes	—
87	C₂²×C₄	—	13	1	no	—
88	C₂²×C₄	—	13	2	no	—
89	C₂²×C₄	—	26	1	no	—
90	C₂²×C₄	—	26	1	no	—
91	C₂²×C₄	—	26	2	no	—
92	C₂×C₈	—	13	2	no	—
93	C₂×C₈	—	13	4	no	—
94	C₂×C₈	—	13	4	no	—
95	C₂×C₈	C₂×#261	1	2	yes	—
96	C₄⋊C₄	—	26	2	no	—
97	C₄⋊C₄	—	26	2	no	—
98	C₄⋊C₄	—	26	2	no	—
99	C₄⋊C₄	—	26	2	no	—
100	C₄⋊C₄	—	52	4	no	—
101	C₄²	—	13	2	no	—
102	C₄²	—	13	1	no	—
103	C₄²	C₂×#261	1	1	yes	characteristic
104	C₁₃	#1847	1	1	yes	characteristic, complemented, Sylow
105	C₂³	—	13	1	no	—
106	C₂×C₄	—	13	1	no	—
107	C₂×C₄	—	13	2	no	—
108	C₂×C₄	—	13	2	no	—
109	C₂×C₄	—	13	2	no	—
110	C₂×C₄	—	26	2	no	—
111	C₂×C₄	—	26	2	no	—
112	C₂×C₄	—	52	1	no	—
113	C₂×C₄	—	52	2	no	—
114	C₂×C₄	—	52	1	no	—
115	C₂×C₄	—	52	4	no	—
116	C₂×C₄	—	52	2	no	—
117	C₂×C₄	—	52	2	no	—
118	C₂×C₄	C₄⋊#261	1	2	yes	—
119	C₂×C₄	C₂²×#261	1	1	yes	characteristic
120	C₈	—	13	4	no	—
121	C₈	C₄⋊#261	1	4	yes	complemented
122	C₂²	—	13	1	no	—
123	C₂²	—	13	1	no	—
124	C₂²	—	13	2	no	—
125	C₂²	—	13	2	no	—
126	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	13	2	no	—
129	C₄	—	26	2	no	—
130	C₄	—	104	2	no	—
131	C₄	—	104	1	no	—
132	C₄	—	104	1	no	—
133	C₄	C₂×C₄⋊#261	1	2	yes	—
134	C₂	—	13	1	no	—
135	C₂	—	13	1	no	—
136	C₂	—	13	2	no	—
137	C₂	#11719059	1	1	yes	characteristic
138	C₂	#11719098	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88102

C₂

yes

maximal

C₂×#88101

C₂

yes

maximal

#11719060

C₂

yes

maximal, characteristic

#11719059

C₂

yes

maximal, characteristic

D₁₃×#97

C₂

yes

maximal, characteristic

C₂×C₄⋊#261

—

C₂×C₄⋊#261

C₂²

yes

—

C₂×C₄⋊#261

C₂²

yes

characteristic

C₂×C₄⋊#261

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

characteristic

(C₂×#261)⋊C₄

—

#88102

—

#88101

—

C₁₃×#97

C₄

yes

characteristic, complemented

#88055

C₄

yes

complemented

#88043

C₄

yes

characteristic, complemented

C₂²×#261

—

C₂²×#261

—

C₂²×#261

—

C₂×C₄×D₁₃

D₄

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

—

—

—

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

Q₈

yes

—

C₂×#1055

C₂×C₄

yes

—

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

#1847

—

maximal, Sylow

C₂²×D₁₃

C₂×D₄

yes

—

—

—

—

—

—

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

C₂×D₄

yes

—

C₄×D₁₃

C₂×Q₈

yes

—

C₈×C₁₃

C₄⋊C₄

yes

complemented

#1055

C₄⋊C₄

yes

complemented

C₂×#107

—

C₂×#106

—

C₂×#97

—

#384

—

#382

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₃

#127

yes

characteristic

C₂×D₁₃

C₄⋊Q₈

yes

characteristic

C₂×D₁₃

AGL(1,ℤ/8)

yes

—

C₂×D₁₃

#137

yes

—

#261

—

#261

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

—

Dic₁₃

—

Dic₁₃

C₄⋊Q₈

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

—

—

—

—

yes

characteristic, complemented

#95

—

C₂×C₁₃

#384

yes

characteristic

C₂×C₁₃

#428

yes

—

D₁₃

yes

D₁₃

yes

D₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

—

103

C₄²

C₂×#261

yes

characteristic

104

C₁₃

#1847

yes

characteristic, complemented, Sylow

105

C₂³

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₄⋊#261

yes

—

119

C₂×C₄

C₂²×#261

yes

characteristic

120

C₈

—

121

C₈

C₄⋊#261

yes

complemented

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×C₄⋊#261

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

104

—

131

C₄

—

104

—

132

C₄

—

104

—

133

C₄

C₂×C₄⋊#261

yes

—

134

C₂

—

135

C₂

—

136

C₂

—

137

C₂

#11719059

yes

characteristic

138

C₂

#11719098

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#1847
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#97

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₃

C₂×D₄

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
15. C₁₃×#97	C₄	semidirect
16. #88055	C₄	semidirect
17. #88043	C₄	semidirect
51. C₈×C₁₃	C₄⋊C₄	semidirect
52. #1055	C₄⋊C₄	semidirect
80. #97	#261	semidirect
104. C₁₃	#1847	semidirect
121. C₈	C₄⋊#261	semidirect

H ≅ G/N

type

15. C₁₃×#97

C₄

semidirect

16. #88055

C₄

semidirect

17. #88043

C₄

semidirect

51. C₈×C₁₃

C₄⋊C₄

semidirect

52. #1055

C₄⋊C₄

semidirect

80. #97

#261

semidirect

104. C₁₃

#1847

semidirect

121. C₈

C₄⋊#261

semidirect

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

subgroup	index
C₂×#88102	2
C₂×#88101	2
#11719060	2
#11719059	2
D₁₃×#97	2
#1847	13

subgroup

index

D₁₃×#97

Subgroups — #13130774

Conjugacy classes of subgroups

Complements

Maximal subgroups