Group #13130773 — subgroups

Subgroups — #13130773

Order 1664.

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

normal subgroups only

This group has 248 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	2	yes	maximal
4	C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊#261	C₂²	1	4	yes	—
6	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	(C₂×#261)⋊C₄	—	2	4	no	—
10	#88102	—	2	4	no	—
11	#88101	—	2	4	no	—
12	C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
14	C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
15	C₄×#1055	C₄	1	1	yes	characteristic, complemented
16	C₂²×#261	—	2	4	no	—
17	C₂×C₄×D₁₃	D₄	1	2	yes	—
18	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
19	C₄⋊#261	—	2	4	no	—
20	C₄⋊#261	—	2	4	no	—
21	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₁₃	Q₈	1	2	yes	—
26	C₂×#1055	C₂×C₄	1	1	yes	characteristic
27	C₂×#1055	C₂×C₄	1	1	yes	characteristic
28	C₈×D₁₃	D₄	1	2	yes	—
29	C₈×D₁₃	D₄	1	2	yes	—
30	C₈×D₁₃	Q₈	1	2	yes	—
31	C₈×D₁₃	Q₈	1	2	yes	—
32	#1846	—	13	1	no	maximal, Sylow
33	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×#261	—	4	4	no	—
35	C₂×#261	—	4	8	no	—
36	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
37	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
40	C₄×D₁₃	—	2	4	no	—
41	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
42	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
43	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
44	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
46	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
47	#1055	C₄⋊C₄	1	2	yes	—
48	#1055	C₄⋊C₄	1	2	yes	—
49	C₂×#107	—	13	2	no	—
50	C₂×#106	—	13	2	no	—
51	C₂×C₄×C₈	—	13	1	no	—
52	#382	—	13	2	no	—
53	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂×D₁₃	#127	1	1	yes	characteristic
55	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
56	C₂×D₁₃	#135	1	4	yes	—
57	#261	—	8	4	no	—
58	C₄×C₁₃	—	2	2	no	—
59	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	Dic₁₃	—	2	2	no	—
62	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
63	Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
64	C₂²×C₈	—	13	1	no	—
65	C₂²×C₈	—	13	1	no	—
66	C₂×C₄⋊C₄	—	13	4	no	—
67	C₂×C₄²	—	13	1	no	—
68	#107	—	26	4	no	—
69	#106	—	26	4	no	—
70	C₄×C₈	—	13	1	no	—
71	C₄×C₈	—	13	1	no	—
72	C₄×C₈	—	13	1	no	—
73	C₄×C₈	#261	1	1	yes	characteristic, complemented
74	#95	—	26	4	no	—
75	C₂×C₁₃	#384	1	1	yes	characteristic
76	C₂×C₁₃	#427	1	2	yes	—
77	D₁₃	#495	1	2	yes	—
78	D₁₃	#499	1	2	yes	—
79	C₂²×C₄	—	13	1	no	—
80	C₂²×C₄	—	13	2	no	—
81	C₂²×C₄	—	26	4	no	—
82	C₂×C₈	—	13	1	no	—
83	C₂×C₈	—	13	1	no	—
84	C₂×C₈	—	13	2	no	—
85	C₂×C₈	—	13	2	no	—
86	C₂×C₈	—	13	2	no	—
87	C₂×C₈	—	13	2	no	—
88	C₂×C₈	C₂×#261	1	1	yes	characteristic
89	C₂×C₈	C₂×#261	1	1	yes	characteristic
90	C₄⋊C₄	—	26	4	no	—
91	C₄⋊C₄	—	26	4	no	—
92	C₄²	—	13	2	no	—
93	C₄²	—	13	1	no	—
94	C₄²	C₂×#261	1	1	yes	characteristic
95	C₁₃	#1846	1	1	yes	characteristic, complemented, Sylow
96	C₂³	—	13	1	no	—
97	C₂×C₄	—	13	1	no	—
98	C₂×C₄	—	13	1	no	—
99	C₂×C₄	—	13	1	no	—
100	C₂×C₄	—	13	1	no	—
101	C₂×C₄	—	13	1	no	—
102	C₂×C₄	—	13	2	no	—
103	C₂×C₄	—	26	4	no	—
104	C₂×C₄	—	52	4	no	—
105	C₂×C₄	—	52	8	no	—
106	C₂×C₄	C₄⋊#261	1	2	yes	—
107	C₂×C₄	C₂²×#261	1	1	yes	characteristic
108	C₈	—	13	2	no	—
109	C₈	—	13	2	no	—
110	C₈	C₄⋊#261	1	2	yes	—
111	C₈	C₄⋊#261	1	2	yes	—
112	C₂²	—	13	1	no	—
113	C₂²	—	13	1	no	—
114	C₂²	—	13	4	no	—
115	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
116	C₄	—	2	2	no	—
117	C₄	—	13	1	no	—
118	C₄	—	13	1	no	—
119	C₄	—	26	2	no	—
120	C₄	—	104	4	no	—
121	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
122	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
123	C₂	—	13	2	no	—
124	C₂	—	13	2	no	—
125	C₂	#11719059	1	1	yes	characteristic
126	C₂	#11719092	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

C₄×C₈×D₁₃

C₂

yes

maximal, characteristic

C₂×C₄⋊#261

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

C₄²×D₁₃

C₂²

yes

characteristic

(C₂×#261)⋊C₄

—

#88102

—

#88101

—

C₄×C₈×C₁₃

C₄

yes

characteristic, complemented

C₈×Dic₁₃

C₄

yes

characteristic, complemented

C₈×Dic₁₃

C₄

yes

characteristic, complemented

C₄×#1055

C₄

yes

characteristic, complemented

C₂²×#261

—

C₂×C₄×D₁₃

D₄

yes

—

C₂×C₄×D₁₃

C₂³

yes

characteristic

C₄⋊#261

—

C₄⋊#261

—

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

Q₈

yes

—

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

C₈×D₁₃

Q₈

yes

—

#1846

—

maximal, Sylow

C₂²×D₁₃

C₂×D₄

yes

characteristic

C₂×#261

—

C₂×#261

—

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

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

C₄×D₁₃

C₂×Q₈

yes

characteristic

C₈×C₁₃

C₄⋊C₄

yes

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

#1055

C₄⋊C₄

yes

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

—

#382

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₃

#127

yes

characteristic

C₂×D₁₃

C₄⋊Q₈

yes

characteristic

C₂×D₁₃

#135

yes

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

C₄⋊Q₈

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

#107

—

#106

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#261

yes

characteristic, complemented

#95

—

C₂×C₁₃

#384

yes

characteristic

C₂×C₁₃

#427

yes

—

D₁₃

#495

yes

—

D₁₃

#499

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₃

#1846

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₄⋊#261

yes

—

107

C₂×C₄

C₂²×#261

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

C₄⋊#261

yes

—

111

C₈

C₄⋊#261

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

—

115

C₂²

C₂×C₄⋊#261

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

104

—

121

C₄

C₂×C₄⋊#261

yes

characteristic

122

C₄

C₂×C₄⋊#261

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

#11719059

yes

characteristic

126

C₂

#11719092

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄×C₈	#261
hypocenter	C₁₃	#1846
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₄×C₈×C₁₃

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₃

C₂×D₄

cosocle

C₂×C₄×D₁₃

C₂³

C₄×C₈

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
12. C₄×C₈×C₁₃	C₄	semidirect
13. C₈×Dic₁₃	C₄	semidirect
14. C₈×Dic₁₃	C₄	semidirect
15. C₄×#1055	C₄	semidirect
73. C₄×C₈	#261	semidirect
95. C₁₃	#1846	semidirect

H ≅ G/N

type

12. C₄×C₈×C₁₃

C₄

semidirect

13. C₈×Dic₁₃

C₄

semidirect

14. C₈×Dic₁₃

C₄

semidirect

15. C₄×#1055

C₄

semidirect

73. C₄×C₈

#261

semidirect

95. C₁₃

#1846

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
C₄×C₈×D₁₃	2
#1846	13

subgroup

index

C₄×C₈×D₁₃

Subgroups — #13130773

Conjugacy classes of subgroups

Complements

Maximal subgroups