Group #15765773 — subgroups

Subgroups — #15765773

Order 3328.

538 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11718342	C₂	1	3	yes	maximal
2	#13115797	C₂	1	3	yes	maximal
3	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#88123	C₂²	1	3	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
6	C₂×#88056	—	2	6	no	—
7	#11718596	C₂²	1	1	yes	characteristic
8	#11718342	—	2	6	no	—
9	#11718342	—	2	6	no	—
10	#11718143	—	2	6	no	—
11	C₂²×Dic₂₆	—	2	3	no	—
12	C₂²×C₈×C₁₃	D₄	1	6	yes	—
13	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄⋊Dic₁₃	—	2	3	no	—
15	C₂×C₄⋊Dic₁₃	—	2	3	no	—
16	C₂×C₄⋊Dic₁₃	—	2	3	no	—
17	#88123	—	2	3	no	—
18	#88123	—	2	3	no	—
19	#88123	—	2	3	no	—
20	#88123	D₄	1	6	yes	—
21	C₄×C₈×C₁₃	—	2	3	no	—
22	C₄×C₈×C₁₃	—	2	3	no	—
23	#88056	—	2	24	no	—
24	#10319	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
26	C₂²×Dic₁₃	—	4	3	no	—
27	C₂²×Dic₁₃	—	4	1	no	—
28	C₂×Dic₂₆	—	2	6	no	—
29	C₂×Dic₂₆	—	4	6	no	—
30	C₂×Dic₂₆	—	4	6	no	—
31	C₂×Dic₂₆	—	4	3	no	—
32	C₂×C₈×C₁₃	—	2	6	no	—
33	C₂×C₈×C₁₃	—	2	6	no	—
34	C₂×C₈×C₁₃	—	2	6	no	—
35	C₄²×C₁₃	C₂×D₄	1	3	yes	—
36	C₄²×C₁₃	#41	1	1	yes	characteristic
37	C₄⋊Dic₁₃	—	2	6	no	—
38	C₄⋊Dic₁₃	—	2	6	no	—
39	C₄⋊Dic₁₃	—	4	3	no	—
40	C₄⋊Dic₁₃	—	4	3	no	—
41	C₄⋊Dic₁₃	—	4	6	no	—
42	C₂×#487	—	13	3	no	—
43	#1990	—	13	3	no	—
44	#1273	D₁₃	1	1	yes	characteristic
45	C₂³×C₁₃	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₃	#120	1	3	yes	—
47	C₂×C₄×C₁₃	#121	1	3	yes	—
48	C₂×C₄×C₁₃	#135	1	6	yes	—
49	C₂×C₄×C₁₃	#137	1	6	yes	—
50	C₂×Dic₁₃	—	4	6	no	—
51	C₂×Dic₁₃	—	8	3	no	—
52	C₂×Dic₁₃	—	8	3	no	—
53	C₂×Dic₁₃	—	8	3	no	—
54	Dic₂₆	—	4	12	no	—
55	Dic₂₆	—	8	6	no	—
56	C₈×C₁₃	—	4	6	no	—
57	C₂×C₄⋊Q₈	—	13	3	no	—
58	#487	—	26	6	no	—
59	#487	—	26	6	no	—
60	C₂×#103	—	26	6	no	—
61	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
62	#384	—	13	1	no	—
63	#340	—	26	6	no	—
64	C₂²×C₁₃	#392	1	1	yes	characteristic
65	C₂²×C₁₃	#495	1	3	yes	—
66	C₂²×C₁₃	#497	1	3	yes	—
67	C₄×C₁₃	#452	1	6	yes	—
68	C₄×C₁₃	#464	1	6	yes	—
69	Dic₁₃	—	8	6	no	—
70	Dic₁₃	—	16	1	no	—
71	C₂²×Q₈	—	26	3	no	—
72	C₂²×C₈	D₅₂	1	6	yes	—
73	C₄⋊Q₈	—	13	6	no	—
74	C₄⋊Q₈	—	26	3	no	—
75	C₄⋊Q₈	—	26	3	no	—
76	C₄⋊Q₈	—	26	3	no	—
77	C₂×C₄⋊C₄	—	26	3	no	—
78	C₂×C₄⋊C₄	—	26	3	no	—
79	C₂×C₄⋊C₄	—	26	3	no	—
80	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
81	#103	—	26	24	no	—
82	C₄×C₈	—	2	3	no	—
83	C₄×C₈	—	2	3	no	—
84	C₂×C₁₃	#1711	1	1	yes	characteristic
85	C₂×C₁₃	#1718	1	3	yes	—
86	C₂×C₁₃	#2015	1	3	yes	—
87	C₂×Q₈	—	26	6	no	—
88	C₂×Q₈	—	52	3	no	—
89	C₂×Q₈	—	52	6	no	—
90	C₂×Q₈	—	52	6	no	—
91	C₂²×C₄	—	52	3	no	—
92	C₂²×C₄	—	52	1	no	—
93	C₂²×C₄	C₂×D₅₂	1	3	yes	—
94	C₂×C₈	—	2	6	no	—
95	C₂×C₈	—	2	6	no	—
96	C₂×C₈	—	2	6	no	—
97	C₄⋊C₄	—	26	6	no	—
98	C₄⋊C₄	—	26	6	no	—
99	C₄⋊C₄	—	52	3	no	—
100	C₄⋊C₄	—	52	3	no	—
101	C₄⋊C₄	—	52	6	no	—
102	C₄²	D₄×D₁₃	1	3	yes	—
103	C₄²	#6131	1	1	yes	characteristic
104	C₁₃	#10319	1	1	yes	characteristic, complemented, Sylow
105	C₂³	#88128	1	1	yes	characteristic
106	Q₈	—	52	12	no	—
107	Q₈	—	104	6	no	—
108	C₂×C₄	—	52	6	no	—
109	C₂×C₄	—	104	3	no	—
110	C₂×C₄	—	104	3	no	—
111	C₂×C₄	—	104	3	no	—
112	C₂×C₄	#88136	1	3	yes	—
113	C₂×C₄	#88149	1	3	yes	—
114	C₂×C₄	#88158	1	6	yes	—
115	C₂×C₄	#88163	1	6	yes	—
116	C₈	—	4	6	no	—
117	C₂²	#11718332	1	1	yes	characteristic
118	C₂²	#11718357	1	3	yes	—
119	C₂²	#11718376	1	3	yes	—
120	C₄	—	104	6	no	—
121	C₄	—	208	1	no	—
122	C₄	#11718394	1	6	yes	—
123	C₄	#11718506	1	6	yes	—
124	C₂	#13114448	1	1	yes	characteristic
125	C₂	#13114482	1	3	yes	—
126	C₂	#13115933	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718342

C₂

yes

maximal

#13115797

C₂

yes

maximal

C₁₃×#1273

C₂

yes

maximal, characteristic

C₂×#88123

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×#88056

—

#11718596

C₂²

yes

—

—

—

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

—

—

—

D₄

yes

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

—

#88056

—

#10319

—

maximal, Sylow

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#487

—

#1990

—

#1273

D₁₃

yes

C₂³×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

C₂×C₄⋊Q₈

—

#487

—

#487

—

C₂×#103

—

C₂×C₄×C₈

C₂×D₁₃

yes

—

#384

—

#340

—

C₂²×C₁₃

#392

yes

characteristic

C₂²×C₁₃

#495

yes

—

C₂²×C₁₃

#497

yes

—

C₄×C₁₃

#452

yes

—

C₄×C₁₃

#464

yes

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

—

C₂²×C₈

D₅₂

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

#103

—

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

#1711

yes

characteristic

C₂×C₁₃

#1718

yes

—

C₂×C₁₃

#2015

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₅₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄²

D₄×D₁₃

yes

—

103

C₄²

#6131

yes

characteristic

104

C₁₃

#10319

yes

characteristic, complemented, Sylow

105

C₂³

#88128

yes

characteristic

106

Q₈

—

107

Q₈

—

104

—

108

C₂×C₄

—

109

C₂×C₄

—

104

—

110

C₂×C₄

—

104

—

111

C₂×C₄

—

104

—

112

C₂×C₄

#88136

yes

—

113

C₂×C₄

#88149

yes

—

114

C₂×C₄

#88158

yes

—

115

C₂×C₄

#88163

yes

—

116

C₈

—

117

C₂²

#11718332

yes

characteristic

118

C₂²

#11718357

yes

—

119

C₂²

#11718376

yes

—

120

C₄

—

104

—

121

C₄

—

208

—

122

C₄

#11718394

yes

—

123

C₄

#11718506

yes

—

124

C₂

#13114448

yes

characteristic

125

C₂

#13114482

yes

—

126

C₂

#13115933

yes

—

	subgroup	G/H
center	C₂³	#88128
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1273	C₂
socle, prime radical	C₂³×C₁₃	#127
hypercenter	#1273	D₁₃
hypocenter	C₁₃	#10319
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center

C₂³

#88128

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1273

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
104. C₁₃	#10319	semidirect

H ≅ G/N

type

104. C₁₃

#10319

semidirect

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

subgroup	index
C₂×#11718342	2
#13115797	2
C₁₃×#1273	2
#10319	13

subgroup

index

C₂×#11718342

#13115797

C₁₃×#1273

#10319

Subgroups — #15765773

Conjugacy classes of subgroups

Complements

Maximal subgroups