Group #15699249 — subgroups

Subgroups — C₁₃×#12910 #15699249

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	4	yes	maximal
2	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1848	C₂	1	2	yes	maximal
4	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
5	C₂×C₁₃×#108	—	2	2	no	—
6	C₂×C₁₃×#108	C₂²	1	4	yes	—
7	C₁₃×#423	—	2	2	no	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#368	—	2	8	no	—
10	C₁₃×#346	C₄	1	4	yes	—
11	C₂×C₁₃×M₁₆	—	2	4	no	—
12	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
16	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
17	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
18	C₁₃×#108	—	2	8	no	—
19	C₁₃×#108	—	4	4	no	—
20	C₁₃×C₄⋊C₈	—	4	4	no	—
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	Q₈	1	2	yes	—
23	#12910	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
25	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₁₃×M₁₆	—	4	4	no	—
27	C₁₃×M₁₆	—	4	4	no	—
28	C₂×C₈×C₁₃	—	4	4	no	—
29	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₈×C₁₃	D₈	1	2	yes	—
31	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
34	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
35	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
37	C₄²×C₁₃	D₈	1	2	yes	—
38	C₁₃×C₁₆	C₄⋊C₄	1	8	yes	—
39	C₂×#368	C₂×C₁₃	1	4	yes	—
40	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
41	#1848	C₂×C₁₃	1	2	yes	—
42	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₃	—	4	2	no	—
44	C₂×C₄×C₁₃	#107	1	4	yes	—
45	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
51	C₈×C₁₃	—	8	4	no	—
52	C₈×C₁₃	#107	1	4	yes	—
53	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
54	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
55	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
56	C₂×#108	—	2	2	no	—
57	C₂×#108	C₂²×C₁₃	1	4	yes	—
58	#423	—	2	2	no	—
59	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
60	#368	—	2	8	no	—
61	#346	C₄×C₁₃	1	4	yes	—
62	C₂²×C₁₃	—	2	2	no	—
63	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
64	C₂²×C₁₃	#494	1	1	yes	characteristic
65	C₂²×C₁₃	#500	1	1	yes	characteristic
66	C₄×C₁₃	—	2	4	no	—
67	C₄×C₁₃	#384	1	1	yes	characteristic
68	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
69	C₄×C₁₃	#493	1	1	yes	characteristic
70	C₄×C₁₃	#500	1	1	yes	characteristic
71	C₂×M₁₆	—	2	4	no	—
72	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
73	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
74	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
75	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
76	C₂×C₁₆	D₄×C₁₃	1	4	yes	—
77	C₂×C₁₆	Q₈×C₁₃	1	4	yes	—
78	#108	—	2	8	no	—
79	#108	—	4	4	no	—
80	C₄⋊C₈	—	4	4	no	—
81	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
82	C₄×C₈	Q₈×C₁₃	1	2	yes	—
83	C₂×C₁₃	—	2	1	no	—
84	C₂×C₁₃	—	2	1	no	—
85	C₂×C₁₃	#1845	1	1	yes	characteristic
86	C₂×C₁₃	#2161	1	2	yes	—
87	C₂²×C₄	C₁₃×Q₁₆	1	2	yes	—
88	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
89	M₁₆	—	4	4	no	—
90	M₁₆	—	4	4	no	—
91	C₂×C₈	—	4	4	no	—
92	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
93	C₂×C₈	C₁₃×D₈	1	2	yes	—
94	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
95	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
96	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
97	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
98	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
99	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
100	C₄²	C₁₃×D₈	1	2	yes	—
101	C₁₆	C₁₃×C₄⋊C₄	1	8	yes	—
102	C₁₃	#12910	1	1	yes	characteristic, direct product factor, Sylow
103	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	C₁₃×#107	1	4	yes	—
106	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
108	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
109	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
110	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
111	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
112	C₈	—	8	4	no	—
113	C₈	C₁₃×#107	1	4	yes	—
114	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
115	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
116	C₂²	—	2	2	no	—
117	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
118	C₂²	C₁₃×#494	1	1	yes	characteristic
119	C₂²	C₁₃×#500	1	1	yes	characteristic
120	C₄	—	2	4	no	—
121	C₄	C₁₃×#384	1	1	yes	characteristic
122	C₄	C₂×C₁₃×#107	1	1	yes	characteristic
123	C₄	C₁₃×#493	1	1	yes	characteristic
124	C₄	C₁₃×#500	1	1	yes	characteristic
125	C₂	—	2	1	no	—
126	C₂	—	2	1	no	—
127	C₂	C₁₃×#1845	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

C₁₃×#1848

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₁₃×#108

—

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#423

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#368

—

C₁₃×#346

C₄

yes

—

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×C₄

yes

—

C₂×C₁₃×C₁₆

D₄

yes

—

C₂×C₁₃×C₁₆

Q₈

yes

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#12910

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

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

D₈

yes

—

C₂×C₈×C₁₃

Q₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

—

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

D₈

yes

—

C₁₃×C₁₆

C₄⋊C₄

yes

—

C₂×#368

C₂×C₁₃

yes

—

C₂×#346

C₂×C₁₃

yes

characteristic

#1848

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

#127

yes

characteristic

C₂×C₄×C₁₃

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₁₆

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

#107

yes

—

C₈×C₁₃

C₂×C₄⋊C₄

yes

—

C₈×C₁₃

C₄⋊Q₈

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×#108

—

C₂×#108

C₂²×C₁₃

yes

—

#423

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#368

—

#346

C₄×C₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₂²×C₁₃

yes

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

D₄×C₁₃

yes

characteristic

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

C₂×C₁₆

D₄×C₁₃

yes

—

C₂×C₁₆

Q₈×C₁₃

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#1845

yes

characteristic

C₂×C₁₃

#2161

yes

—

C₂²×C₄

C₁₃×Q₁₆

yes

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×D₈

yes

—

C₂×C₈

C₁₃×Q₁₆

yes

—

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

C₂×D₄×C₁₃

yes

—

C₂×C₈

C₂×Q₈×C₁₃

yes

—

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

C₄²

C₁₃×C₄⋊C₄

yes

—

100

C₄²

C₁₃×D₈

yes

—

101

C₁₆

C₁₃×C₄⋊C₄

yes

—

102

C₁₃

#12910

yes

characteristic, direct product factor, Sylow

103

C₂³

C₂×C₁₃×Q₁₆

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

C₁₃×#107

yes

—

106

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

107

C₂×C₄

C₁₃×#127

yes

characteristic

108

C₂×C₄

C₁₃×C₄⋊Q₈

yes

characteristic

109

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

110

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

111

C₂×C₄

C₂×C₁₃×Q₁₆

yes

characteristic

112

C₈

—

113

C₈

C₁₃×#107

yes

—

114

C₈

C₂×C₁₃×C₄⋊C₄

yes

—

115

C₈

C₁₃×C₄⋊Q₈

yes

—

116

C₂²

—

117

C₂²

C₂×C₁₃×#107

yes

characteristic

118

C₂²

C₁₃×#494

yes

characteristic

119

C₂²

C₁₃×#500

yes

characteristic

120

C₄

—

121

C₄

C₁₃×#384

yes

characteristic

122

C₄

C₂×C₁₃×#107

yes

characteristic

123

C₄

C₁₃×#493

yes

characteristic

124

C₄

C₁₃×#500

yes

characteristic

125

C₂

—

126

C₂

—

127

C₂

C₁₃×#1845

yes

characteristic

128

C₂

C₁₃×#2161

yes

—

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

C₂×C₈

C₂²×C₄×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
23. #12910	C₁₃	direct (N × H)
102. C₁₃	#12910	direct (N × H)

H ≅ G/N

type

23. #12910

C₁₃

direct (N × H)

102. C₁₃

#12910

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
C₁₃×#1848	2
#12910	13

subgroup

index

C₂×C₁₃×#368

C₂×C₁₃×#346

C₁₃×#1848

#12910

Subgroups — C₁₃×#12910 #15699249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12910 #15699249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12910 #15699249