Group #15699015 — subgroups

Subgroups — C₁₃×#12676 #15699015

Order 3328.

306 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 190 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×#368	C₂	1	2	yes	maximal
2	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#108	C₂	1	2	yes	maximal
4	C₁₃×#1381	C₂	1	2	yes	maximal
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	4	yes	—
8	C₄×C₁₃×M₁₆	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#368	C₄	1	8	yes	complemented
11	C₁₃×#346	C₄	1	4	yes	—
12	C₁₃×#341	—	2	2	no	—
13	C₂×C₁₃×M₁₆	—	2	4	no	—
14	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	—	2	2	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
21	C₁₃×#108	—	2	4	no	—
22	C₁₃×#108	C₂×C₄	1	8	yes	—
23	C₁₃×#97	—	4	2	no	—
24	C₄×C₈×C₁₃	—	4	2	no	—
25	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₃	Q₈	1	2	yes	—
27	#12676	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
29	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₁₃×M₁₆	—	2	8	no	—
31	C₁₃×M₁₆	—	4	4	no	—
32	C₂×C₈×C₁₃	—	2	2	no	—
33	C₂×C₈×C₁₃	—	4	4	no	—
34	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	#41	1	2	yes	—
39	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
40	C₄²×C₁₃	D₈	1	2	yes	—
41	C₁₃×C₁₆	—	2	2	no	—
42	C₁₃×C₁₆	C₄²	1	4	yes	—
43	C₂×#368	C₂×C₁₃	1	2	yes	—
44	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
45	C₄×#108	C₂×C₁₃	1	2	yes	—
46	#1381	C₂×C₁₃	1	2	yes	—
47	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₃	—	4	2	no	—
49	C₂×C₄×C₁₃	#107	1	4	yes	—
50	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
53	C₂×C₄×C₁₃	#135	1	2	yes	—
54	C₈×C₁₃	—	2	2	no	—
55	C₈×C₁₃	—	4	8	no	—
56	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
57	C₈×C₁₃	#117	1	1	yes	characteristic
58	C₈×C₁₃	C₄×Q₈	1	2	yes	—
59	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
60	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
61	C₂×#108	C₂²×C₁₃	1	4	yes	—
62	C₄×M₁₆	—	2	2	no	—
63	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
64	#368	C₄×C₁₃	1	8	yes	complemented
65	#346	C₄×C₁₃	1	4	yes	—
66	#341	—	2	2	no	—
67	C₂²×C₁₃	—	2	2	no	—
68	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
69	C₂²×C₁₃	C₄×Q₁₆	1	2	yes	—
70	C₄×C₁₃	—	2	4	no	—
71	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
72	C₄×C₁₃	#427	1	1	yes	characteristic
73	C₄×C₁₃	C₄×D₈	1	2	yes	—
74	C₂×M₁₆	—	2	4	no	—
75	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
76	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
77	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
78	C₂×C₁₆	—	2	2	no	—
79	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
80	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
81	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
82	#108	—	2	4	no	—
83	#108	C₂×C₄×C₁₃	1	8	yes	—
84	#97	—	4	2	no	—
85	C₄×C₈	—	4	2	no	—
86	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
87	C₄×C₈	Q₈×C₁₃	1	2	yes	—
88	C₂×C₁₃	—	2	2	no	—
89	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
90	C₂×C₁₃	#2161	1	2	yes	—
91	C₂²×C₄	C₁₃×Q₁₆	1	2	yes	—
92	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
93	M₁₆	—	2	8	no	—
94	M₁₆	—	4	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	4	4	no	—
97	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
98	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
99	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
100	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
101	C₂×C₈	C₁₃×#41	1	2	yes	—
102	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
103	C₄²	C₁₃×D₈	1	2	yes	—
104	C₁₆	—	2	2	no	—
105	C₁₆	C₄²×C₁₃	1	4	yes	—
106	C₁₃	#12676	1	1	yes	characteristic, direct product factor, Sylow
107	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	C₁₃×#107	1	4	yes	—
110	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
112	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
113	C₂×C₄	C₁₃×#135	1	2	yes	—
114	C₈	—	2	2	no	—
115	C₈	—	4	8	no	—
116	C₈	C₂×C₄²×C₁₃	1	1	yes	characteristic
117	C₈	C₁₃×#117	1	1	yes	characteristic
118	C₈	C₄×Q₈×C₁₃	1	2	yes	—
119	C₂²	—	2	2	no	—
120	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
121	C₂²	C₄×C₁₃×Q₁₆	1	2	yes	—
122	C₄	—	2	4	no	—
123	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
124	C₄	C₁₃×#427	1	1	yes	characteristic
125	C₄	C₄×C₁₃×D₈	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	C₄×C₁₃×#107	1	1	yes	characteristic
128	C₂	C₁₃×#2161	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#368

C₂

yes

maximal

C₂×C₁₃×#346

C₂

yes

maximal, characteristic

C₄×C₁₃×#108

C₂

yes

maximal

C₁₃×#1381

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂²×C₁₃×C₁₆

C₂²

yes

characteristic

C₂×C₁₃×#108

C₂²

yes

—

C₄×C₁₃×M₁₆

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#368

C₄

yes

complemented

C₁₃×#346

C₄

yes

—

C₁₃×#341

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₁₃×#108

—

C₁₃×#108

C₂×C₄

yes

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#12676

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

D₈

yes

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₄²

yes

—

C₂×#368

C₂×C₁₃

yes

—

C₂×#346

C₂×C₁₃

yes

characteristic

C₄×#108

C₂×C₁₃

yes

—

#1381

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₄×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

#135

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

C₂×C₄²

yes

characteristic

C₈×C₁₃

#117

yes

characteristic

C₈×C₁₃

C₄×Q₈

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

characteristic

C₂²×C₁₆

C₂²×C₁₃

yes

characteristic

C₂×#108

C₂²×C₁₃

yes

—

C₄×M₁₆

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#368

C₄×C₁₃

yes

complemented

#346

C₄×C₁₃

yes

—

#341

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#107

yes

characteristic

C₂²×C₁₃

C₄×Q₁₆

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₄×C₄⋊C₄

yes

characteristic

C₄×C₁₃

#427

yes

characteristic

C₄×C₁₃

C₄×D₈

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

D₄×C₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

#108

—

#108

C₂×C₄×C₁₃

yes

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

C₄×#107

yes

characteristic

C₂×C₁₃

#2161

yes

—

C₂²×C₄

C₁₃×Q₁₆

yes

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

C₂²×C₄×C₁₃

yes

—

100

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

101

C₂×C₈

C₁₃×#41

yes

—

102

C₄²

C₁₃×C₄⋊C₄

yes

—

103

C₄²

C₁₃×D₈

yes

—

104

C₁₆

—

105

C₁₆

C₄²×C₁₃

yes

—

106

C₁₃

#12676

yes

characteristic, direct product factor, Sylow

107

C₂³

C₂×C₁₃×Q₁₆

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

C₁₃×#107

yes

—

110

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

111

C₂×C₄

C₄×D₄×C₁₃

yes

—

112

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

113

C₂×C₄

C₁₃×#135

yes

—

114

C₈

—

115

C₈

—

116

C₈

C₂×C₄²×C₁₃

yes

characteristic

117

C₈

C₁₃×#117

yes

characteristic

118

C₈

C₄×Q₈×C₁₃

yes

—

119

C₂²

—

120

C₂²

C₂×C₁₃×#107

yes

characteristic

121

C₂²

C₄×C₁₃×Q₁₆

yes

—

122

C₄

—

123

C₄

C₄×C₁₃×C₄⋊C₄

yes

characteristic

124

C₄

C₁₃×#427

yes

characteristic

125

C₄

C₄×C₁₃×D₈

yes

—

126

C₂

—

127

C₂

C₄×C₁₃×#107

yes

characteristic

128

C₂

C₁₃×#2161

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₈	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₃

C₂×D₈

commutator

C₈

C₂×C₄²×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
10. C₁₃×#368	C₄	semidirect
27. #12676	C₁₃	direct (N × H)
64. #368	C₄×C₁₃	semidirect
106. C₁₃	#12676	direct (N × H)

H ≅ G/N

type

10. C₁₃×#368

C₄

semidirect

27. #12676

C₁₃

direct (N × H)

64. #368

C₄×C₁₃

semidirect

106. C₁₃

#12676

direct (N × H)

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

subgroup	index
C₂×C₁₃×#368	2
C₂×C₁₃×#346	2
C₄×C₁₃×#108	2
C₁₃×#1381	2
#12676	13

subgroup

index

C₂×C₁₃×#368

C₂×C₁₃×#346

C₄×C₁₃×#108

C₁₃×#1381

#12676

Subgroups — C₁₃×#12676 #15699015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12676 #15699015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12676 #15699015