Group #15699987 — subgroups

Subgroups — C₁₃×#13648 #15699987

Order 3328.

184 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 118 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	C₁₃×#2258	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2170	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1422	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1401	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#504	C₂²	1	2	yes	—
7	C₁₃×#443	C₄	1	1	yes	characteristic
8	C₁₃×M₆₄	—	2	2	no	—
9	C₁₃×M₆₄	C₂²	1	2	yes	—
10	C₂×C₁₃×C₃₂	—	2	2	no	—
11	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
13	C₁₃×#364	C₄	1	1	yes	characteristic
14	C₁₃×#350	C₄	1	2	yes	—
15	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
16	C₁₃×#135	C₈	1	1	yes	characteristic
17	C₁₃×#131	C₂×C₄	1	2	yes	—
18	C₁₃×M₃₂	—	2	2	no	—
19	C₁₃×M₃₂	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	—	2	2	no	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
23	C₁₃×#108	C₈	1	1	yes	characteristic
24	C₁₃×#104	C₈	1	2	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₁₃×C₃₂	—	2	2	no	—
27	C₁₃×C₃₂	—	2	1	no	—
28	C₁₃×C₃₂	D₄	1	2	yes	—
29	#13648	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₁₃×#41	C₂×C₈	1	2	yes	—
31	C₁₃×Q₁₆	C₁₆	1	1	yes	characteristic
32	C₁₃×SD₁₆	C₁₆	1	2	yes	—
33	C₁₃×D₈	C₁₆	1	1	yes	characteristic
34	C₁₃×M₁₆	—	2	2	no	—
35	C₁₃×M₁₆	C₂×C₈	1	2	yes	—
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
40	C₁₃×C₁₆	—	2	2	no	—
41	C₁₃×C₁₆	—	2	1	no	—
42	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
43	C₁₃×C₁₆	#41	1	1	yes	characteristic
44	#2258	C₂×C₁₃	1	2	yes	complemented
45	#2170	C₂×C₁₃	1	1	yes	characteristic
46	#1422	C₂×C₁₃	1	1	yes	characteristic, complemented
47	#1401	C₂×C₁₃	1	2	yes	complemented
48	#1397	C₂×C₁₃	1	1	yes	characteristic, complemented
49	Q₈×C₁₃	C₂×C₁₆	1	2	yes	—
50	D₄×C₁₃	—	2	2	no	—
51	D₄×C₁₃	C₂×C₁₆	1	2	yes	—
52	C₂×C₄×C₁₃	—	2	2	no	—
53	C₂×C₄×C₁₃	—	2	1	no	—
54	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
55	C₈×C₁₃	—	2	2	no	—
56	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
57	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
58	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
59	C₈×C₁₃	#131	1	1	yes	characteristic
60	#504	C₂²×C₁₃	1	2	yes	—
61	#443	C₄×C₁₃	1	1	yes	characteristic
62	M₆₄	—	2	2	no	—
63	M₆₄	C₂²×C₁₃	1	2	yes	—
64	C₂×C₃₂	—	2	2	no	—
65	C₂×C₃₂	C₂²×C₁₃	1	1	yes	characteristic
66	C₂×C₃₂	C₂²×C₁₃	1	1	yes	characteristic
67	#364	C₄×C₁₃	1	1	yes	characteristic
68	#350	C₄×C₁₃	1	2	yes	—
69	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
70	C₂²×C₁₃	—	2	2	no	—
71	C₂²×C₁₃	#504	1	1	yes	characteristic
72	C₄×C₁₃	—	2	2	no	—
73	C₄×C₁₃	—	4	1	no	—
74	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
75	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
76	#135	C₈×C₁₃	1	1	yes	characteristic
77	#131	C₂×C₄×C₁₃	1	2	yes	—
78	M₃₂	—	2	2	no	—
79	M₃₂	C₂×C₄×C₁₃	1	2	yes	—
80	C₂×C₁₆	—	2	2	no	—
81	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
82	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
83	#108	C₈×C₁₃	1	1	yes	characteristic
84	#104	C₈×C₁₃	1	2	yes	—
85	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
86	C₃₂	—	2	2	no	—
87	C₃₂	—	2	1	no	—
88	C₃₂	D₄×C₁₃	1	2	yes	—
89	C₂×C₁₃	—	2	1	no	—
90	C₂×C₁₃	—	4	2	no	—
91	C₂×C₁₃	D₄×C₁₆	1	1	yes	characteristic
92	#41	C₂×C₈×C₁₃	1	2	yes	—
93	Q₁₆	C₁₃×C₁₆	1	1	yes	characteristic
94	SD₁₆	C₁₃×C₁₆	1	2	yes	—
95	D₈	C₁₃×C₁₆	1	1	yes	characteristic
96	M₁₆	—	2	2	no	—
97	M₁₆	C₂×C₈×C₁₃	1	2	yes	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
100	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
101	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
102	C₁₆	—	2	2	no	—
103	C₁₆	—	2	1	no	—
104	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
105	C₁₆	C₁₃×#41	1	1	yes	characteristic
106	C₁₃	#13648	1	1	yes	characteristic, direct product factor, Sylow
107	Q₈	C₂×C₁₃×C₁₆	1	2	yes	—
108	D₄	—	2	2	no	—
109	D₄	C₂×C₁₃×C₁₆	1	2	yes	—
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	1	no	—
112	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	C₂×C₁₃×C₁₆	1	1	yes	characteristic
115	C₈	C₂×C₁₃×C₁₆	1	1	yes	characteristic
116	C₈	C₄×D₄×C₁₃	1	1	yes	characteristic
117	C₈	C₁₃×#131	1	1	yes	characteristic
118	C₂²	—	2	2	no	—
119	C₂²	C₁₃×#504	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	—	4	1	no	—
122	C₄	C₈×D₄×C₁₃	1	1	yes	characteristic
123	C₄	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
124	C₂	—	2	1	no	—
125	C₂	—	4	2	no	—
126	C₂	D₄×C₁₃×C₁₆	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2258

C₂

yes

maximal, complemented

C₁₃×#2170

C₂

yes

maximal, characteristic

C₁₃×#1422

C₂

yes

maximal, characteristic, complemented

C₁₃×#1401

C₂

yes

maximal, complemented

C₁₃×#1397

C₂

yes

maximal, characteristic, complemented

C₁₃×#504

C₂²

yes

—

C₁₃×#443

C₄

yes

characteristic

C₁₃×M₆₄

—

C₁₃×M₆₄

C₂²

yes

—

C₂×C₁₃×C₃₂

—

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

C₂×C₁₃×C₃₂

C₂²

yes

characteristic

C₁₃×#364

C₄

yes

characteristic

C₁₃×#350

C₄

yes

—

C₄×C₁₃×C₁₆

C₂²

yes

characteristic

C₁₃×#135

C₈

yes

characteristic

C₁₃×#131

C₂×C₄

yes

—

C₁₃×M₃₂

—

C₁₃×M₃₂

C₂×C₄

yes

—

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

C₂³

yes

characteristic

C₁₃×#108

C₈

yes

characteristic

C₁₃×#104

C₈

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₁₃×C₃₂

—

C₁₃×C₃₂

—

C₁₃×C₃₂

D₄

yes

—

#13648

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₁₃×#41

C₂×C₈

yes

—

C₁₃×Q₁₆

C₁₆

yes

characteristic

C₁₃×SD₁₆

C₁₆

yes

—

C₁₃×D₈

C₁₆

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

C₂×C₈

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₈

yes

characteristic

C₁₃×C₁₆

—

C₁₃×C₁₆

—

C₁₃×C₁₆

C₂×D₄

yes

C₁₃×C₁₆

yes

C₂×C₁₃

yes

complemented

#2170

C₂×C₁₃

yes

characteristic

#1422

C₂×C₁₃

yes

characteristic, complemented

#1401

C₂×C₁₃

yes

complemented

#1397

C₂×C₁₃

yes

characteristic, complemented

Q₈×C₁₃

C₂×C₁₆

yes

—

D₄×C₁₃

—

D₄×C₁₃

C₂×C₁₆

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

C₂×C₁₆

yes

characteristic

C₈×C₁₃

C₂×C₁₆

yes

characteristic

C₈×C₁₃

C₄×D₄

yes

C₈×C₁₃

yes

C₂²×C₁₃

yes

—

#443

C₄×C₁₃

yes

characteristic

M₆₄

—

M₆₄

C₂²×C₁₃

yes

—

C₂×C₃₂

—

C₂×C₃₂

C₂²×C₁₃

yes

characteristic

C₂×C₃₂

C₂²×C₁₃

yes

characteristic

#364

C₄×C₁₃

yes

characteristic

#350

C₄×C₁₃

yes

—

C₄×C₁₆

C₂²×C₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

#504

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₈×D₄

yes

characteristic

C₄×C₁₃

C₂²×C₁₆

yes

characteristic

#135

C₈×C₁₃

yes

characteristic

#131

C₂×C₄×C₁₃

yes

—

M₃₂

—

M₃₂

C₂×C₄×C₁₃

yes

—

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

characteristic

C₂×C₁₆

C₂³×C₁₃

yes

characteristic

#108

C₈×C₁₃

yes

characteristic

#104

C₈×C₁₃

yes

—

C₄×C₈

C₂×C₄×C₁₃

yes

characteristic

C₃₂

—

C₃₂

—

C₃₂

D₄×C₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

D₄×C₁₆

yes

characteristic

#41

C₂×C₈×C₁₃

yes

—

Q₁₆

C₁₃×C₁₆

yes

characteristic

SD₁₆

C₁₃×C₁₆

yes

—

D₈

C₁₃×C₁₆

yes

characteristic

M₁₆

—

M₁₆

C₂×C₈×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

C₂×C₈×C₁₃

yes

characteristic

100

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

101

C₄²

C₂×C₈×C₁₃

yes

characteristic

102

C₁₆

—

103

C₁₆

—

104

C₁₆

C₂×D₄×C₁₃

yes

characteristic

105

C₁₆

C₁₃×#41

yes

characteristic

106

C₁₃

#13648

yes

characteristic, direct product factor, Sylow

107

Q₈

C₂×C₁₃×C₁₆

yes

—

108

D₄

—

109

D₄

C₂×C₁₃×C₁₆

yes

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₂²×C₈×C₁₃

yes

characteristic

113

C₈

—

114

C₈

C₂×C₁₃×C₁₆

yes

characteristic

115

C₈

C₂×C₁₃×C₁₆

yes

characteristic

116

C₈

C₄×D₄×C₁₃

yes

characteristic

117

C₈

C₁₃×#131

yes

characteristic

118

C₂²

—

119

C₂²

C₁₃×#504

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

C₈×D₄×C₁₃

yes

characteristic

123

C₄

C₂²×C₁₃×C₁₆

yes

characteristic

124

C₂

—

125

C₂

—

126

C₂

D₄×C₁₃×C₁₆

yes

characteristic

	subgroup	G/H
center	C₁₃×C₁₆	C₂×D₄
commutator	C₄	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	D₄×C₁₆
prime radical	C₁₃×#135	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₁₆ ◁ C₂×C₁₃×C₃₂ ◁ G

subgroup

G/H

center

C₁₃×C₁₆

C₂×D₄

commutator

C₄

C₂²×C₁₃×C₁₆

Frattini, cosocle

C₂×C₁₆

C₂³×C₁₃

socle

C₂×C₁₃

D₄×C₁₆

prime radical

C₁₃×#135

C₈

LCS

G ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₁₃×C₁₆ ◁ C₂×C₁₃×C₃₂ ◁ G

N	H ≅ G/N	type
1. C₁₃×#2258	C₂	semidirect
3. C₁₃×#1422	C₂	semidirect
4. C₁₃×#1401	C₂	semidirect
5. C₁₃×#1397	C₂	semidirect
29. #13648	C₁₃	direct (N × H)
44. #2258	C₂×C₁₃	semidirect
46. #1422	C₂×C₁₃	semidirect
47. #1401	C₂×C₁₃	semidirect
48. #1397	C₂×C₁₃	semidirect
106. C₁₃	#13648	direct (N × H)

H ≅ G/N

type

1. C₁₃×#2258

C₂

semidirect

3. C₁₃×#1422

C₂

semidirect

4. C₁₃×#1401

C₂

semidirect

5. C₁₃×#1397

C₂

semidirect

29. #13648

C₁₃

direct (N × H)

44. #2258

C₂×C₁₃

semidirect

46. #1422

C₂×C₁₃

semidirect

47. #1401

C₂×C₁₃

semidirect

48. #1397

C₂×C₁₃

semidirect

106. C₁₃

#13648

direct (N × H)

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

subgroup	index
C₁₃×#2258	2
C₁₃×#2170	2
C₁₃×#1422	2
C₁₃×#1401	2
C₁₃×#1397	2
#13648	13

subgroup

index

C₁₃×#2258

C₁₃×#2170

C₁₃×#1422

C₁₃×#1401

C₁₃×#1397

#13648

Subgroups — C₁₃×#13648 #15699987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#13648 #15699987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13648 #15699987