Group #15753372 — subgroups

Subgroups — #15753372

Order 3328.

330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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	#13113128	C₂	1	2	yes	maximal
2	#13112667	C₂	1	2	yes	maximal
3	#13112665	C₂	1	2	yes	maximal
4	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#376	C₂²	1	1	yes	characteristic
10	#11718586	C₂²	1	4	yes	—
11	#11718046	C₄	1	8	yes	complemented
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
17	C₁₃×#97	—	2	4	no	—
18	C₁₃×#97	—	2	2	no	—
19	C₄×C₈×C₁₃	—	2	4	no	—
20	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
21	C₁₃×#95	—	2	2	no	—
22	C₂²⋊#1055	—	2	4	no	—
23	C₄⋊#1055	—	2	4	no	—
24	C₄×#1055	C₂×C₄	1	8	yes	—
25	#8140	—	13	1	no	maximal, Sylow
26	C₂²×C₄×C₁₃	—	2	2	no	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	#41	1	2	yes	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	—	2	2	no	—
32	C₂×C₈×C₁₃	—	2	2	no	—
33	C₂×C₈×C₁₃	C₄²	1	2	yes	—
34	C₂×C₈×C₁₃	C₄²	1	2	yes	—
35	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
36	C₄²×C₁₃	—	2	2	no	—
37	C₄²×C₁₃	M₁₆	1	4	yes	—
38	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
39	C₄²×C₁₃	#41	1	2	yes	—
40	C₂×#1055	—	2	8	no	—
41	#1726	D₁₃	1	1	yes	characteristic
42	#1452	—	13	2	no	—
43	#1275	—	13	2	no	—
44	#1274	—	13	2	no	—
45	C₂³×C₁₃	#117	1	1	yes	characteristic
46	C₂×C₄×C₁₃	—	2	4	no	—
47	C₂×C₄×C₁₃	—	4	2	no	—
48	C₂×C₄×C₁₃	—	4	4	no	—
49	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₃	#117	1	4	yes	—
51	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
52	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
54	C₈×C₁₃	—	2	2	no	—
55	C₈×C₁₃	—	2	2	no	—
56	C₈×C₁₃	—	2	4	no	—
57	#1055	—	4	8	no	—
58	#431	—	13	4	no	—
59	C₂×#97	Dic₁₃	1	2	yes	—
60	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
61	C₂×C₄×C₈	Dic₁₃	1	2	yes	—
62	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
63	#376	C₂×D₁₃	1	1	yes	characteristic
64	#322	—	13	8	no	—
65	C₂²×C₁₃	—	2	2	no	—
66	C₂²×C₁₃	#376	1	1	yes	characteristic
67	C₂²×C₁₃	#432	1	2	yes	—
68	C₄×C₁₃	—	2	4	no	—
69	C₄×C₁₃	—	4	4	no	—
70	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
71	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
72	C₄×C₁₃	#432	1	2	yes	—
73	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
74	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
75	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
76	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
77	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
78	C₄⋊C₈	—	26	4	no	—
79	C₂²⋊C₈	—	26	4	no	—
80	#97	—	2	4	no	—
81	#97	—	2	2	no	—
82	C₄×C₈	—	2	4	no	—
83	C₄×C₈	—	13	8	no	—
84	C₄×C₈	C₄×D₁₃	1	4	yes	—
85	#95	—	2	2	no	—
86	C₂×C₁₃	—	2	2	no	—
87	C₂×C₁₃	#1745	1	1	yes	characteristic
88	C₂×C₁₃	#1747	1	2	yes	—
89	C₂²×C₄	—	2	2	no	—
90	C₂²×C₄	#6127	1	2	yes	—
91	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	26	8	no	—
97	C₂×C₈	#6099	1	4	yes	—
98	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
99	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
100	C₄²	—	2	2	no	—
101	C₄²	#6099	1	4	yes	—
102	C₄²	C₂×C₄×D₁₃	1	2	yes	—
103	C₄²	#6127	1	2	yes	—
104	C₁₃	#8140	1	1	yes	characteristic, complemented, Sylow
105	C₂³	#88180	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	4	no	—
109	C₂×C₄	#88126	1	4	yes	—
110	C₂×C₄	C₂×#6099	1	2	yes	—
111	C₂×C₄	C₂×#6099	1	2	yes	—
112	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
113	C₂×C₄	#88180	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	2	2	no	—
116	C₈	—	2	4	no	—
117	C₈	—	52	8	no	—
118	C₂²	—	2	2	no	—
119	C₂²	#11718587	1	2	yes	—
120	C₂²	#11718593	1	1	yes	characteristic
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₄×#6099	1	1	yes	characteristic
124	C₄	C₄×#6099	1	1	yes	characteristic
125	C₄	#11718587	1	2	yes	—
126	C₂	—	2	2	no	—
127	C₂	#13114585	1	1	yes	characteristic
128	C₂	#13114591	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13113128

C₂

yes

maximal

#13112667

C₂

yes

maximal

#13112665

C₂

yes

maximal

C₁₃×#1726

C₂

yes

maximal, characteristic

C₂×C₁₃×#97

C₄

yes

—

C₂×C₁₃×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#376

C₂²

yes

characteristic

#11718586

C₂²

yes

—

#11718046

C₄

yes

complemented

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#97

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₁₃×#95

—

C₂²⋊#1055

—

C₄⋊#1055

—

C₄×#1055

C₂×C₄

yes

—

#8140

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

C₄²

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

M₁₆

yes

—

C₄²×C₁₃

C₂²×C₄

yes

—

C₄²×C₁₃

#41

yes

—

C₂×#1055

—

#1726

D₁₃

yes

—

—

—

C₂³×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#431

—

C₂×#97

Dic₁₃

yes

—

C₂×#97

C₂×D₁₃

yes

characteristic

C₂×C₄×C₈

Dic₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#376

C₂×D₁₃

yes

characteristic

#322

—

C₂²×C₁₃

—

C₂²×C₁₃

#376

yes

characteristic

C₂²×C₁₃

#432

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₄×M₁₆

yes

characteristic

C₄×C₁₃

C₄×M₁₆

yes

characteristic

C₄×C₁₃

#432

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

characteristic

C₂²×C₈

C₂×Dic₁₃

yes

characteristic

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₃

yes

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#1745

yes

characteristic

C₂×C₁₃

#1747

yes

—

C₂²×C₄

—

C₂²×C₄

#6127

yes

—

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#6099

yes

—

C₂×C₈

C₄×Dic₁₃

yes

—

C₂×C₈

C₄×Dic₁₃

yes

—

100

C₄²

—

101

C₄²

#6099

yes

—

102

C₄²

C₂×C₄×D₁₃

yes

—

103

C₄²

#6127

yes

—

104

C₁₃

#8140

yes

characteristic, complemented, Sylow

105

C₂³

#88180

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#88126

yes

—

110

C₂×C₄

C₂×#6099

yes

—

111

C₂×C₄

C₂×#6099

yes

—

112

C₂×C₄

C₂×C₄×Dic₁₃

yes

characteristic

113

C₂×C₄

#88180

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

117

C₈

—

118

C₂²

—

119

C₂²

#11718587

yes

—

120

C₂²

#11718593

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

C₄×#6099

yes

characteristic

124

C₄

C₄×#6099

yes

characteristic

125

C₄

#11718587

yes

—

126

C₂

—

127

C₂

#13114585

yes

characteristic

128

C₂

#13114591

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1726	C₂
socle	C₂²×C₁₃	#376
prime radical	C₂³×C₁₃	#117
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1726	D₁₃
hypocenter	C₁₃	#8140
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #1726

subgroup

G/H

center

C₂×C₄

C₂×C₄×Dic₁₃

commutator

C₂×C₄×C₁₃

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1726

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ #1726

N	H ≅ G/N	type
11. #11718046	C₄	semidirect
104. C₁₃	#8140	semidirect

H ≅ G/N

type

11. #11718046

C₄

semidirect

104. C₁₃

#8140

semidirect

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

subgroup	index
#13113128	2
#13112667	2
#13112665	2
C₁₃×#1726	2
#8140	13

subgroup

index

C₁₃×#1726

Subgroups — #15753372

Conjugacy classes of subgroups

Complements

Maximal subgroups