Group #15779283 — subgroups

Subgroups — #15779283

Order 3328.

302 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 155 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	#13116592	C₂	1	2	yes	maximal
2	#13112918	C₂	1	4	yes	maximal
3	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#97	C₄	1	2	yes	—
5	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#376	C₄	1	1	yes	characteristic
9	C₂×#88052	C₂²	1	4	yes	—
10	C₄⋊#6090	—	2	4	no	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₁₃×#97	—	2	4	no	—
17	C₁₃×#97	C₈	1	4	yes	—
18	C₄×C₈×C₁₃	—	2	4	no	—
19	C₄×C₈×C₁₃	D₄	1	2	yes	—
20	C₄×C₈×C₁₃	Q₈	1	2	yes	—
21	C₁₃×#95	—	2	2	no	—
22	#88052	—	2	8	no	—
23	C₂×#6090	—	2	4	no	—
24	#12884	—	13	1	no	maximal, Sylow
25	C₂²×C₄×C₁₃	—	2	2	no	—
26	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	#41	1	4	yes	—
36	C₄²×C₁₃	—	2	2	no	—
37	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₄²×C₁₃	C₂×C₈	1	2	yes	—
39	C₄²×C₁₃	M₁₆	1	4	yes	—
40	#6090	—	4	4	no	—
41	#2150	—	13	2	no	—
42	#1726	D₁₃	1	1	yes	characteristic
43	#1376	—	13	4	no	—
44	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	2	4	no	—
46	C₂×C₄×C₁₃	—	4	2	no	—
47	C₂×C₄×C₁₃	—	4	4	no	—
48	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
49	C₂×C₄×C₁₃	C₂×C₄⋊C₄	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	2	no	—
54	C₈×C₁₃	—	2	4	no	—
55	C₈×C₁₃	#124	1	2	yes	—
56	C₈×C₁₃	#125	1	2	yes	—
57	C₂×M₃₂	—	13	4	no	—
58	C₂×#97	Dic₁₃	1	2	yes	—
59	C₂×#97	Dic₁₃	1	1	yes	characteristic
60	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
61	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
62	#376	Dic₁₃	1	1	yes	characteristic
63	C₄⋊C₁₆	—	26	4	no	—
64	C₂²×C₁₃	—	2	2	no	—
65	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
66	C₂²×C₁₃	#432	1	2	yes	—
67	C₄×C₁₃	—	2	4	no	—
68	C₄×C₁₃	—	4	4	no	—
69	C₄×C₁₃	#382	1	1	yes	characteristic
70	C₄×C₁₃	#423	1	1	yes	characteristic
71	C₄×C₁₃	#431	1	2	yes	—
72	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
73	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
74	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
75	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
76	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
77	M₃₂	—	26	8	no	—
78	C₂×C₁₆	—	26	4	no	—
79	#97	—	2	4	no	—
80	#97	#1055	1	4	yes	—
81	C₄×C₈	—	2	4	no	—
82	C₄×C₈	Dic₂₆	1	2	yes	—
83	C₄×C₈	D₅₂	1	2	yes	—
84	#95	—	2	2	no	—
85	C₂×C₁₃	—	2	2	no	—
86	C₂×C₁₃	#1831	1	1	yes	characteristic
87	C₂×C₁₃	#2153	1	2	yes	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	#6099	1	2	yes	—
90	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	C₂×#1055	1	4	yes	—
95	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
96	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
97	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
98	C₂×C₈	#6127	1	4	yes	—
99	C₄²	—	2	2	no	—
100	C₄²	C₂×#1055	1	2	yes	—
101	C₄²	#6099	1	4	yes	—
102	C₄²	C₄⋊Dic₁₃	1	2	yes	—
103	C₁₆	—	52	4	no	—
104	C₁₃	#12884	1	1	yes	characteristic, complemented, Sylow
105	C₂³	C₂×#6099	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	C₄⋊#1055	1	4	yes	—
110	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
111	C₂×C₄	C₂×#6099	1	2	yes	—
112	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
113	C₂×C₄	#88180	1	2	yes	—
114	C₈	—	2	2	no	—
115	C₈	—	2	4	no	—
116	C₈	#88124	1	2	yes	—
117	C₈	#88129	1	2	yes	—
118	C₂²	—	2	2	no	—
119	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
120	C₂²	#11718587	1	2	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	#11718585	1	1	yes	characteristic
124	C₄	#11718586	1	2	yes	—
125	C₄	#11718597	1	1	yes	characteristic
126	C₂	—	2	2	no	—
127	C₂	#13114953	1	1	yes	characteristic
128	C₂	#13116602	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13116592

C₂

yes

maximal

#13112918

C₂

yes

maximal

C₁₃×#1726

C₂

yes

maximal, characteristic

C₂×C₁₃×#97

C₄

yes

—

C₂×C₁₃×#97

C₄

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#376

C₄

yes

characteristic

C₂×#88052

C₂²

yes

—

C₄⋊#6090

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₁₃×#97

—

C₁₃×#97

C₈

yes

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₁₃×#95

—

—

—

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

M₁₆

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

C₂×C₈

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

C₂×C₈

yes

—

C₄²×C₁₃

M₁₆

yes

—

#6090

—

#2150

—

#1726

D₁₃

yes

characteristic

#1376

—

C₂³×C₁₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#124

yes

—

C₈×C₁₃

#125

yes

—

C₂×M₃₂

—

C₂×#97

Dic₁₃

yes

—

C₂×#97

Dic₁₃

yes

characteristic

C₂×C₄×C₈

C₂×D₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#376

Dic₁₃

yes

characteristic

C₄⋊C₁₆

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#432

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

characteristic

C₂²×C₈

C₂²×D₁₃

yes

characteristic

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

M₃₂

—

C₂×C₁₆

—

#97

—

#97

#1055

yes

—

C₄×C₈

—

C₄×C₈

Dic₂₆

yes

—

C₄×C₈

D₅₂

yes

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#1831

yes

characteristic

C₂×C₁₃

#2153

yes

—

C₂²×C₄

—

C₂²×C₄

#6099

yes

—

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#1055

yes

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₂×C₈

C₂×Dic₂₆

yes

characteristic

C₂×C₈

C₂×D₅₂

yes

characteristic

C₂×C₈

#6127

yes

—

C₄²

—

100

C₄²

C₂×#1055

yes

—

101

C₄²

#6099

yes

—

102

C₄²

C₄⋊Dic₁₃

yes

—

103

C₁₆

—

104

C₁₃

#12884

yes

characteristic, complemented, Sylow

105

C₂³

C₂×#6099

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊#1055

yes

—

110

C₂×C₄

C₂²×#1055

yes

characteristic

111

C₂×C₄

C₂×#6099

yes

—

112

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

113

C₂×C₄

#88180

yes

—

114

C₈

—

115

C₈

—

116

C₈

#88124

yes

—

117

C₈

#88129

yes

—

118

C₂²

—

119

C₂²

C₂×C₄⋊#1055

yes

characteristic

120

C₂²

#11718587

yes

—

121

C₄

—

122

C₄

—

123

C₄

#11718585

yes

characteristic

124

C₄

#11718586

yes

—

125

C₄

#11718597

yes

characteristic

126

C₂

—

127

C₂

#13114953

yes

characteristic

128

C₂

#13116602

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1726	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1726	D₁₃
hypocenter	C₁₃	#12884
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

subgroup

G/H

center

C₂×C₈

C₂×D₅₂

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1726

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂³×C₁₃

C₂×M₁₆

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

N	H ≅ G/N	type
104. C₁₃	#12884	semidirect

H ≅ G/N

type

104. C₁₃

#12884

semidirect

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

subgroup	index
#13116592	2
#13112918	2
C₁₃×#1726	2
#12884	13

subgroup

index

#13116592

#13112918

C₁₃×#1726

#12884

Subgroups — #15779283

Conjugacy classes of subgroups

Complements

Maximal subgroups