Group #13110596 — subgroups

Subgroups — C₂×C₁₃×#331 #13110596

Order 1664.

360 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 136 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×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₁₃×#331	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₄×C₁₃	—	2	2	no	—
5	C₂²×D₄×C₁₃	C₄	1	2	yes	—
6	C₂²×C₈×C₁₃	—	2	2	no	—
7	C₁₃×#127	—	2	2	no	—
8	C₁₃×#127	C₄	1	2	yes	—
9	C₁₃×#127	C₂²	1	2	yes	—
10	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×C₄⋊C₈	—	2	2	no	—
12	C₁₃×C₄⋊C₈	C₂²	1	4	yes	complemented
13	C₂⁴×C₁₃	—	2	2	no	—
14	C₂×D₄×C₁₃	—	2	2	no	—
15	C₂×D₄×C₁₃	—	2	4	no	—
16	C₂×D₄×C₁₃	—	2	4	no	—
17	C₂×D₄×C₁₃	—	4	4	no	—
18	C₂×D₄×C₁₃	—	4	4	no	—
19	C₂×D₄×C₁₃	—	4	4	no	—
20	C₂×D₄×C₁₃	C₂×C₄	1	4	yes	—
21	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₃	D₄	1	2	yes	—
23	C₂×C₈×C₁₃	—	2	4	no	—
24	C₂×C₈×C₁₃	—	4	4	no	—
25	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₁₃	D₄	1	2	yes	—
27	C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×#331	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂³×C₁₃	—	2	4	no	—
30	C₂³×C₁₃	—	4	4	no	—
31	C₂³×C₁₃	—	4	8	no	—
32	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
33	D₄×C₁₃	—	4	4	no	—
34	D₄×C₁₃	—	4	4	no	—
35	D₄×C₁₃	—	4	8	no	—
36	D₄×C₁₃	—	4	4	no	—
37	D₄×C₁₃	—	4	4	no	—
38	C₂×C₄×C₁₃	—	2	2	no	—
39	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₃	D₈	1	4	yes	—
42	C₂×C₄×C₁₃	SD₁₆	1	4	yes	—
43	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
45	C₈×C₁₃	—	4	4	no	—
46	C₂×#127	C₂×C₁₃	1	1	yes	characteristic
47	C₂×C₄⋊C₈	C₂×C₁₃	1	2	yes	complemented
48	#331	C₂×C₁₃	1	4	yes	direct product factor
49	C₂²×C₁₃	—	4	4	no	—
50	C₂²×C₁₃	—	4	8	no	—
51	C₂²×C₁₃	—	8	8	no	—
52	C₂²×C₁₃	#100	1	2	yes	—
53	C₂²×C₁₃	#102	1	4	yes	—
54	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₄×C₁₃	—	2	1	no	—
56	C₄×C₁₃	—	2	1	no	—
57	C₄×C₁₃	#102	1	4	yes	—
58	C₄×C₁₃	C₂×D₈	1	2	yes	—
59	C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
60	C₂²×D₄	—	2	2	no	—
61	C₂²×D₄	C₄×C₁₃	1	2	yes	—
62	C₂²×C₈	—	2	2	no	—
63	#127	—	2	2	no	—
64	#127	C₄×C₁₃	1	2	yes	—
65	#127	C₂²×C₁₃	1	2	yes	—
66	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
67	C₄⋊C₈	—	2	2	no	—
68	C₄⋊C₈	C₂²×C₁₃	1	4	yes	complemented
69	C₂×C₁₃	—	8	4	no	—
70	C₂×C₁₃	#331	1	4	yes	direct product factor
71	C₂×C₁₃	C₂×#100	1	1	yes	characteristic
72	C₂×C₁₃	C₂×#102	1	2	yes	—
73	C₂⁴	—	2	2	no	—
74	C₂×D₄	—	2	2	no	—
75	C₂×D₄	—	2	4	no	—
76	C₂×D₄	—	2	4	no	—
77	C₂×D₄	—	4	4	no	—
78	C₂×D₄	—	4	4	no	—
79	C₂×D₄	—	4	4	no	—
80	C₂×D₄	C₂×C₄×C₁₃	1	4	yes	—
81	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
82	C₂²×C₄	D₄×C₁₃	1	2	yes	—
83	C₂×C₈	—	2	4	no	—
84	C₂×C₈	—	4	4	no	—
85	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
86	C₄²	D₄×C₁₃	1	2	yes	—
87	C₄²	C₂³×C₁₃	1	1	yes	characteristic
88	C₁₃	C₂×#331	1	1	yes	characteristic, direct product factor, Sylow
89	C₂³	—	2	4	no	—
90	C₂³	—	4	4	no	—
91	C₂³	—	4	8	no	—
92	C₂³	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
93	D₄	—	4	4	no	—
94	D₄	—	4	4	no	—
95	D₄	—	4	8	no	—
96	D₄	—	4	4	no	—
97	D₄	—	4	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
101	C₂×C₄	C₁₃×D₈	1	4	yes	—
102	C₂×C₄	C₁₃×SD₁₆	1	4	yes	—
103	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
104	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
105	C₈	—	4	4	no	—
106	C₂²	—	4	4	no	—
107	C₂²	—	4	8	no	—
108	C₂²	—	8	8	no	—
109	C₂²	C₁₃×#100	1	2	yes	—
110	C₂²	C₁₃×#102	1	4	yes	—
111	C₂²	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	C₁₃×#102	1	4	yes	—
115	C₄	C₂×C₁₃×D₈	1	2	yes	—
116	C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
117	C₂	—	8	4	no	—
118	C₂	C₁₃×#331	1	4	yes	direct product factor
119	C₂	C₂×C₁₃×#100	1	1	yes	characteristic
120	C₂	C₂×C₁₃×#102	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#127

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊C₈

C₂

yes

maximal, complemented

C₁₃×#331

C₂

yes

maximal, direct product factor

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

C₄

yes

—

C₂²×C₈×C₁₃

—

C₁₃×#127

—

C₁₃×#127

C₄

yes

—

C₁₃×#127

C₂²

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×C₄⋊C₈

C₂²

yes

complemented

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

C₂³

yes

characteristic

C₂×#331

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂²⋊C₄

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

D₈

yes

—

C₂×C₄×C₁₃

SD₁₆

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₈×C₁₃

—

C₂×#127

C₂×C₁₃

yes

characteristic

C₂×C₄⋊C₈

C₂×C₁₃

yes

complemented

#331

C₂×C₁₃

yes

direct product factor

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#100

yes

—

C₂²×C₁₃

#102

yes

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#102

yes

—

C₄×C₁₃

C₂×D₈

yes

—

C₄×C₁₃

C₂×SD₁₆

yes

—

C₂²×D₄

—

C₂²×D₄

C₄×C₁₃

yes

—

C₂²×C₈

—

#127

—

#127

C₄×C₁₃

yes

—

#127

C₂²×C₁₃

yes

—

C₂×C₄²

C₂²×C₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₃

yes

complemented

C₂×C₁₃

—

C₂×C₁₃

#331

yes

direct product factor

C₂×C₁₃

C₂×#100

yes

characteristic

C₂×C₁₃

C₂×#102

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×C₄×C₁₃

yes

—

C₂²×C₄

C₂×C₄×C₁₃

yes

characteristic

C₂²×C₄

D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₄²

C₂×C₄×C₁₃

yes

characteristic

C₄²

D₄×C₁₃

yes

—

C₄²

C₂³×C₁₃

yes

characteristic

C₁₃

C₂×#331

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₁₃×C₂²⋊C₄

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

C₁₃×C₂²⋊C₄

yes

characteristic

100

C₂×C₄

C₁₃×C₂²⋊C₄

yes

—

101

C₂×C₄

C₁₃×D₈

yes

—

102

C₂×C₄

C₁₃×SD₁₆

yes

—

103

C₂×C₄

C₂²×C₄×C₁₃

yes

characteristic

104

C₂×C₄

C₂×D₄×C₁₃

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

—

108

C₂²

—

109

C₂²

C₁₃×#100

yes

—

110

C₂²

C₁₃×#102

yes

—

111

C₂²

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

C₁₃×#102

yes

—

115

C₄

C₂×C₁₃×D₈

yes

—

116

C₄

C₂×C₁₃×SD₁₆

yes

—

117

C₂

—

118

C₂

C₁₃×#331

yes

direct product factor

119

C₂

C₂×C₁₃×#100

yes

characteristic

120

C₂

C₂×C₁₃×#102

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

C₂²⋊C₄

commutator

C₂×C₄

C₂²×C₄×C₁₃

Frattini, cosocle

C₄²

C₂³×C₁₃

prime radical

C₂×C₁₃×#127

C₂

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₂×C₁₃×C₄⋊C₈	C₂	semidirect
3. C₁₃×#331	C₂	direct (N × H)
12. C₁₃×C₄⋊C₈	C₂²	semidirect
28. C₂×#331	C₁₃	direct (N × H)
47. C₂×C₄⋊C₈	C₂×C₁₃	semidirect
48. #331	C₂×C₁₃	direct (N × H)
68. C₄⋊C₈	C₂²×C₁₃	semidirect
70. C₂×C₁₃	#331	direct (N × H)
88. C₁₃	C₂×#331	direct (N × H)
118. C₂	C₁₃×#331	direct (N × H)

H ≅ G/N

type

2. C₂×C₁₃×C₄⋊C₈

C₂

semidirect

3. C₁₃×#331

C₂

direct (N × H)

12. C₁₃×C₄⋊C₈

C₂²

semidirect

28. C₂×#331

C₁₃

direct (N × H)

47. C₂×C₄⋊C₈

C₂×C₁₃

semidirect

48. #331

C₂×C₁₃

direct (N × H)

68. C₄⋊C₈

C₂²×C₁₃

semidirect

70. C₂×C₁₃

#331

direct (N × H)

88. C₁₃

C₂×#331

direct (N × H)

118. C₂

C₁₃×#331

direct (N × H)

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

subgroup	index
C₂×C₁₃×#127	2
C₂×C₁₃×C₄⋊C₈	2
C₁₃×#331	2
C₂×#331	13

subgroup

index

C₂×C₁₃×#127

C₂×C₁₃×C₄⋊C₈

C₁₃×#331

C₂×#331

Subgroups — C₂×C₁₃×#331 #13110596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C13×#331 #13110596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#331 #13110596