Group #15696550 — subgroups

Subgroups — C₁₃×#10211 #15696550

Order 3328.

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

normal subgroups only

This group has 406 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	C₁₃×#3237	C₂	1	3	yes	maximal
2	C₁₃×#1515	C₂	1	3	yes	maximal
3	C₁₃×#1308	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#533	C₂²	1	3	yes	—
5	C₁₃×#501	—	2	3	no	—
6	C₁₃×#491	—	2	3	no	—
7	C₁₃×#485	—	2	6	no	—
8	C₁₃×#477	—	2	3	no	—
9	C₁₃×#475	—	2	3	no	—
10	C₁₃×#432	C₂²	1	3	yes	—
11	C₁₃×#383	C₂²	1	1	yes	characteristic
12	C₁₃×#328	—	2	6	no	—
13	C₁₃×C₄⋊Q₈	D₄	1	3	yes	—
14	C₁₃×C₄⋊Q₈	D₄	1	3	yes	—
15	C₁₃×#125	—	2	3	no	—
16	C₁₃×C₂²⋊Q₈	—	2	3	no	—
17	C₁₃×C₂²⋊Q₈	—	2	3	no	—
18	C₄×Q₈×C₁₃	—	2	3	no	—
19	C₄×Q₈×C₁₃	—	2	3	no	—
20	C₁₃×#117	—	2	3	no	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×#107	—	2	6	no	—
23	C₁₃×#106	—	2	6	no	—
24	C₁₃×C₄⋊C₈	—	2	3	no	—
25	C₁₃×#103	—	2	6	no	—
26	C₁₃×#103	—	2	6	no	—
27	C₁₃×C₂²⋊C₈	D₄	1	6	yes	—
28	C₁₃×#97	—	2	3	no	—
29	C₁₃×#95	—	2	3	no	—
30	#10211	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×Q₈×C₁₃	—	2	3	no	—
32	C₂×Q₈×C₁₃	—	2	3	no	—
33	C₂²×C₄×C₁₃	—	4	1	no	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
35	C₂×C₈×C₁₃	—	2	6	no	—
36	C₁₃×C₄⋊C₄	—	2	3	no	—
37	C₁₃×C₄⋊C₄	—	2	3	no	—
38	C₁₃×C₄⋊C₄	—	2	3	no	—
39	C₁₃×C₄⋊C₄	—	2	3	no	—
40	C₁₃×C₄⋊C₄	—	4	3	no	—
41	C₁₃×C₄⋊C₄	—	4	3	no	—
42	C₁₃×C₂²⋊C₄	—	4	3	no	—
43	C₄²×C₁₃	—	4	3	no	—
44	C₄²×C₁₃	C₂×D₄	1	3	yes	—
45	C₄²×C₁₃	#41	1	1	yes	characteristic
46	#3237	C₂×C₁₃	1	3	yes	—
47	#1515	C₂×C₁₃	1	3	yes	—
48	#1308	C₂×C₁₃	1	1	yes	characteristic
49	C₂³×C₁₃	#127	1	1	yes	characteristic
50	Q₈×C₁₃	—	4	6	no	—
51	Q₈×C₁₃	—	8	3	no	—
52	C₂×C₄×C₁₃	—	4	3	no	—
53	C₂×C₄×C₁₃	—	4	3	no	—
54	C₂×C₄×C₁₃	—	4	3	no	—
55	C₂×C₄×C₁₃	—	8	3	no	—
56	C₂×C₄×C₁₃	#120	1	3	yes	—
57	C₂×C₄×C₁₃	#121	1	3	yes	—
58	C₈×C₁₃	—	4	6	no	—
59	#533	C₂²×C₁₃	1	3	yes	—
60	#501	—	2	3	no	—
61	#491	—	2	3	no	—
62	#485	—	2	6	no	—
63	#477	—	2	3	no	—
64	#475	—	2	3	no	—
65	#432	C₂²×C₁₃	1	3	yes	—
66	#383	C₂²×C₁₃	1	1	yes	characteristic
67	#328	—	2	6	no	—
68	C₂²×C₁₃	—	2	3	no	—
69	C₂²×C₁₃	#392	1	1	yes	characteristic
70	C₄×C₁₃	—	2	3	no	—
71	C₄×C₁₃	—	2	3	no	—
72	C₄×C₁₃	—	8	3	no	—
73	C₄×C₁₃	—	8	3	no	—
74	C₄×C₁₃	—	16	1	no	—
75	C₄⋊Q₈	D₄×C₁₃	1	3	yes	—
76	C₄⋊Q₈	D₄×C₁₃	1	3	yes	—
77	#125	—	2	3	no	—
78	C₂²⋊Q₈	—	2	3	no	—
79	C₂²⋊Q₈	—	2	3	no	—
80	C₄×Q₈	—	2	3	no	—
81	C₄×Q₈	—	2	3	no	—
82	#117	—	2	3	no	—
83	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
84	#107	—	2	6	no	—
85	#106	—	2	6	no	—
86	C₄⋊C₈	—	2	3	no	—
87	#103	—	2	6	no	—
88	#103	—	2	6	no	—
89	C₂²⋊C₈	D₄×C₁₃	1	6	yes	—
90	#97	—	2	3	no	—
91	#95	—	2	3	no	—
92	C₂×C₁₃	—	4	1	no	—
93	C₂×C₁₃	#2009	1	3	yes	—
94	C₂×Q₈	—	2	3	no	—
95	C₂×Q₈	—	2	3	no	—
96	C₂²×C₄	—	4	1	no	—
97	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
98	C₂×C₈	—	2	6	no	—
99	C₄⋊C₄	—	2	3	no	—
100	C₄⋊C₄	—	2	3	no	—
101	C₄⋊C₄	—	2	3	no	—
102	C₄⋊C₄	—	2	3	no	—
103	C₄⋊C₄	—	4	3	no	—
104	C₄⋊C₄	—	4	3	no	—
105	C₂²⋊C₄	—	4	3	no	—
106	C₄²	—	4	3	no	—
107	C₄²	C₂×D₄×C₁₃	1	3	yes	—
108	C₄²	C₁₃×#41	1	1	yes	characteristic
109	C₁₃	#10211	1	1	yes	characteristic, direct product factor, Sylow
110	C₂³	C₁₃×#127	1	1	yes	characteristic
111	Q₈	—	4	6	no	—
112	Q₈	—	8	3	no	—
113	C₂×C₄	—	4	3	no	—
114	C₂×C₄	—	4	3	no	—
115	C₂×C₄	—	4	3	no	—
116	C₂×C₄	—	8	3	no	—
117	C₂×C₄	C₁₃×#120	1	3	yes	—
118	C₂×C₄	C₁₃×#121	1	3	yes	—
119	C₈	—	4	6	no	—
120	C₂²	—	2	3	no	—
121	C₂²	C₁₃×#392	1	1	yes	characteristic
122	C₄	—	2	3	no	—
123	C₄	—	2	3	no	—
124	C₄	—	8	3	no	—
125	C₄	—	8	3	no	—
126	C₄	—	16	1	no	—
127	C₂	—	4	1	no	—
128	C₂	C₁₃×#2009	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#3237

C₂

yes

maximal

C₁₃×#1515

C₂

yes

maximal

C₁₃×#1308

C₂

yes

maximal, characteristic

C₁₃×#533

C₂²

yes

—

C₁₃×#501

—

C₁₃×#491

—

C₁₃×#485

—

C₁₃×#477

—

C₁₃×#475

—

C₁₃×#432

C₂²

yes

—

C₁₃×#383

C₂²

yes

characteristic

C₁₃×#328

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×C₄⋊Q₈

D₄

yes

—

C₁₃×#125

—

C₁₃×C₂²⋊Q₈

—

C₁₃×C₂²⋊Q₈

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

—

C₁₃×#117

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#107

—

C₁₃×#106

—

C₁₃×C₄⋊C₈

—

C₁₃×#103

—

C₁₃×#103

—

C₁₃×C₂²⋊C₈

D₄

yes

—

C₁₃×#97

—

C₁₃×#95

—

#10211

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

#3237

C₂×C₁₃

yes

—

#1515

C₂×C₁₃

yes

—

#1308

C₂×C₁₃

yes

characteristic

C₂³×C₁₃

#127

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₈×C₁₃

—

#533

C₂²×C₁₃

yes

—

—

—

—

—

—

C₂²×C₁₃

yes

—

#383

C₂²×C₁₃

yes

characteristic

#328

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄⋊Q₈

D₄×C₁₃

yes

—

C₄⋊Q₈

D₄×C₁₃

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂³×C₁₃

yes

characteristic

#107

—

#106

—

C₄⋊C₈

—

#103

—

#103

—

C₂²⋊C₈

D₄×C₁₃

yes

—

#97

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#2009

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₄²

C₂×D₄×C₁₃

yes

—

108

C₄²

C₁₃×#41

yes

characteristic

109

C₁₃

#10211

yes

characteristic, direct product factor, Sylow

110

C₂³

C₁₃×#127

yes

characteristic

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₁₃×#120

yes

—

118

C₂×C₄

C₁₃×#121

yes

—

119

C₈

—

120

C₂²

—

121

C₂²

C₁₃×#392

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₂

—

128

C₂

C₁₃×#2009

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂³×C₁₃

#127

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
30. #10211	C₁₃	direct (N × H)
109. C₁₃	#10211	direct (N × H)

H ≅ G/N

type

30. #10211

C₁₃

direct (N × H)

109. C₁₃

#10211

direct (N × H)

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

subgroup	index
C₁₃×#3237	2
C₁₃×#1515	2
C₁₃×#1308	2
#10211	13

subgroup

index

C₁₃×#3237

C₁₃×#1515

C₁₃×#1308

#10211

Subgroups — C₁₃×#10211 #15696550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10211 #15696550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10211 #15696550