Group #15698930 — subgroups

Subgroups — C₁₃×#12591 #15698930

Order 3328.

390 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 254 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×#346	C₂	1	2	yes	maximal
2	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1374	C₂	1	4	yes	maximal
4	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
5	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₄³×C₁₃	C₄	1	1	yes	characteristic
10	C₁₃×#346	C₄	1	8	yes	complemented
11	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	C₈	1	4	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	—	2	8	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	8	yes	—
19	C₄×C₈×C₁₃	—	2	4	no	—
20	C₄×C₈×C₁₃	—	2	4	no	—
21	C₄×C₈×C₁₃	C₈	1	4	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
23	#12591	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
25	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₃	—	2	2	no	—
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	C₄²	1	2	yes	—
30	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
33	C₂×C₈×C₁₃	#41	1	4	yes	—
34	C₄²×C₁₃	—	2	8	no	—
35	C₄²×C₁₃	—	2	2	no	—
36	C₄²×C₁₃	—	2	2	no	—
37	C₄²×C₁₃	C₄²	1	2	yes	—
38	C₄²×C₁₃	C₂×C₈	1	2	yes	—
39	C₁₃×C₁₆	—	2	8	no	—
40	C₂×#346	C₂×C₁₃	1	2	yes	—
41	C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic
42	#1374	C₂×C₁₃	1	4	yes	—
43	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
44	C₂×C₄×C₁₃	—	2	4	no	—
45	C₂×C₄×C₁₃	—	2	4	no	—
46	C₂×C₄×C₁₃	—	2	4	no	—
47	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
48	C₂×C₄×C₁₃	M₃₂	1	8	yes	—
49	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₃	#117	1	2	yes	—
51	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
53	C₈×C₁₃	—	2	4	no	—
54	C₈×C₁₃	#97	1	4	yes	—
55	C₈×C₁₃	#117	1	4	yes	—
56	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
57	C₂×C₄×C₈	C₄×C₁₃	1	2	yes	—
58	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
59	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
60	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
61	C₄³	C₄×C₁₃	1	1	yes	characteristic
62	#346	C₄×C₁₃	1	8	yes	complemented
63	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
64	C₂²×C₁₃	#431	1	2	yes	—
65	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
66	C₄×C₁₃	—	2	4	no	—
67	C₄×C₁₃	—	2	8	no	—
68	C₄×C₁₃	#376	1	1	yes	characteristic
69	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
70	C₄×C₁₃	#431	1	2	yes	—
71	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
72	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
73	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
74	C₂×C₄²	C₈×C₁₃	1	4	yes	—
75	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
76	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
77	C₂×C₁₆	—	2	8	no	—
78	C₂×C₁₆	C₂×C₄×C₁₃	1	8	yes	—
79	C₄×C₈	—	2	4	no	—
80	C₄×C₈	—	2	4	no	—
81	C₄×C₈	C₈×C₁₃	1	4	yes	—
82	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
83	C₂×C₁₃	#1744	1	1	yes	characteristic
84	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
85	C₂×C₁₃	#2163	1	4	yes	—
86	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
87	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
88	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	C₄²×C₁₃	1	2	yes	—
92	C₂×C₈	C₂×C₈×C₁₃	1	4	yes	—
93	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
94	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
95	C₂×C₈	C₁₃×#41	1	4	yes	—
96	C₄²	—	2	8	no	—
97	C₄²	—	2	2	no	—
98	C₄²	—	2	2	no	—
99	C₄²	C₄²×C₁₃	1	2	yes	—
100	C₄²	C₂×C₈×C₁₃	1	2	yes	—
101	C₁₆	—	2	8	no	—
102	C₁₃	#12591	1	1	yes	characteristic, direct product factor, Sylow
103	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	C₄×C₈×C₁₃	1	4	yes	—
108	C₂×C₄	C₁₃×M₃₂	1	8	yes	—
109	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
110	C₂×C₄	C₁₃×#117	1	2	yes	—
111	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
112	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
113	C₈	—	2	4	no	—
114	C₈	C₁₃×#97	1	4	yes	—
115	C₈	C₁₃×#117	1	4	yes	—
116	C₂²	C₂×C₄×C₈×C₁₃	1	1	yes	characteristic
117	C₂²	C₁₃×#431	1	2	yes	—
118	C₂²	C₂×C₁₃×M₃₂	1	4	yes	—
119	C₄	—	2	4	no	—
120	C₄	—	2	8	no	—
121	C₄	C₁₃×#376	1	1	yes	characteristic
122	C₄	C₂×C₁₃×#97	1	1	yes	characteristic
123	C₄	C₁₃×#431	1	2	yes	—
124	C₂	C₁₃×#1744	1	1	yes	characteristic
125	C₂	C₄×C₁₃×M₃₂	1	2	yes	—
126	C₂	C₁₃×#2163	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#346

C₂

yes

maximal

C₄²×C₈×C₁₃

C₂

yes

maximal, characteristic

C₁₃×#1374

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₄

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₄³×C₁₃

C₄

yes

characteristic

C₁₃×#346

C₄

yes

complemented

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₈

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

C₈

yes

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

#12591

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₄²

yes

—

C₄²×C₁₃

C₂×C₈

yes

—

C₁₃×C₁₆

—

C₂×#346

C₂×C₁₃

yes

—

C₄²×C₈

C₂×C₁₃

yes

characteristic

#1374

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄×C₈

yes

—

C₂×C₄×C₁₃

M₃₂

yes

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

#97

yes

—

C₈×C₁₃

#117

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₄×C₁₃

yes

—

C₂×C₄×C₈

C₄×C₁₃

yes

characteristic

C₂×C₄×C₈

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

C₄³

C₄×C₁₃

yes

characteristic

#346

C₄×C₁₃

yes

complemented

C₂²×C₁₃

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₂²×C₁₃

C₂×M₃₂

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#376

yes

characteristic

C₄×C₁₃

C₂×#97

yes

characteristic

C₄×C₁₃

#431

yes

—

C₂²×C₈

C₂×C₄×C₁₃

yes

—

C₂²×C₈

C₂×C₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

C₈×C₁₃

yes

—

C₂×C₄²

C₂×C₄×C₁₃

yes

—

C₂×C₄²

C₂×C₄×C₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₈×C₁₃

yes

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₂×C₁₃

#1744

yes

characteristic

C₂×C₁₃

C₄×M₃₂

yes

—

C₂×C₁₃

#2163

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₃

yes

—

C₂×C₈

C₂×C₈×C₁₃

yes

—

C₂×C₈

C₁₃×M₁₆

yes

—

C₂×C₈

C₂²×C₄×C₁₃

yes

—

C₂×C₈

C₁₃×#41

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₄²×C₁₃

yes

—

100

C₄²

C₂×C₈×C₁₃

yes

—

101

C₁₆

—

102

C₁₃

#12591

yes

characteristic, direct product factor, Sylow

103

C₂³

C₂²×C₈×C₁₃

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₄×C₈×C₁₃

yes

—

108

C₂×C₄

C₁₃×M₃₂

yes

—

109

C₂×C₄

C₂×C₄²×C₁₃

yes

characteristic

110

C₂×C₄

C₁₃×#117

yes

—

111

C₂×C₄

C₂²×C₈×C₁₃

yes

characteristic

112

C₂×C₄

C₂×C₁₃×M₁₆

yes

—

113

C₈

—

114

C₈

C₁₃×#97

yes

—

115

C₈

C₁₃×#117

yes

—

116

C₂²

C₂×C₄×C₈×C₁₃

yes

characteristic

117

C₂²

C₁₃×#431

yes

—

118

C₂²

C₂×C₁₃×M₃₂

yes

—

119

C₄

—

120

C₄

—

121

C₄

C₁₃×#376

yes

characteristic

122

C₄

C₂×C₁₃×#97

yes

characteristic

123

C₄

C₁₃×#431

yes

—

124

C₂

C₁₃×#1744

yes

characteristic

125

C₂

C₄×C₁₃×M₃₂

yes

—

126

C₂

C₁₃×#2163

yes

—

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

subgroup

G/H

center

C₂²×C₈×C₁₃

C₂³

commutator

C₂²

C₂×C₄×C₈×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle, prime radical

C₂³×C₁₃

C₂²×C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
10. C₁₃×#346	C₄	semidirect
23. #12591	C₁₃	direct (N × H)
62. #346	C₄×C₁₃	semidirect
102. C₁₃	#12591	direct (N × H)

H ≅ G/N

type

10. C₁₃×#346

C₄

semidirect

23. #12591

C₁₃

direct (N × H)

62. #346

C₄×C₁₃

semidirect

102. C₁₃

#12591

direct (N × H)

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

subgroup	index
C₂×C₁₃×#346	2
C₄²×C₈×C₁₃	2
C₁₃×#1374	2
#12591	13

subgroup

index

C₂×C₁₃×#346

C₄²×C₈×C₁₃

C₁₃×#1374

#12591

Subgroups — C₁₃×#12591 #15698930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12591 #15698930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12591 #15698930