Group #15863170 — subgroups

Subgroups — #15863170

Order 3328.

830 conjugacy classes of subgroups; only the 243 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 243 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	D₁₃×#376	C₂	1	1	yes	maximal, characteristic
2	#13114981	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114980	C₂	1	6	yes	maximal, complemented
4	#13114528	C₂	1	6	yes	maximal
5	C₁₃×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6094	C₂²	1	4	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
8	C₁₃×#376	C₂²	1	1	yes	characteristic
9	#11718593	C₂²	1	3	yes	—
10	D₁₃×#95	C₄	1	4	yes	—
11	#11718309	C₄	1	4	yes	—
12	C₁₃×#336	C₂²	1	6	yes	—
13	#11718142	C₂²	1	12	yes	—
14	#11718116	C₂²	1	6	yes	—
15	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
18	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
19	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
21	C₂²×#1055	C₂³	1	4	yes	—
22	C₂×#6094	—	2	24	no	—
23	C₄²×D₁₃	—	2	12	no	—
24	C₁₃×#95	C₂×C₄	1	4	yes	—
25	#88071	C₂×C₄	1	12	yes	—
26	#20773	—	13	1	no	maximal, Sylow
27	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
29	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
31	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×D₁₃	—	2	12	no	—
33	C₂×C₄×D₁₃	—	4	12	no	—
34	C₂×C₄×D₁₃	#41	1	12	yes	—
35	C₂×C₈×C₁₃	—	2	12	no	—
36	C₄²×C₁₃	—	2	6	no	—
37	C₄×Dic₁₃	—	2	6	no	—
38	C₄×Dic₁₃	—	2	12	no	—
39	C₂×#1055	—	2	12	no	—
40	#6094	—	4	16	no	—
41	C₂×#376	—	13	1	no	—
42	#1840	—	13	1	no	—
43	#1840	—	13	6	no	—
44	#1840	D₁₃	1	1	yes	characteristic, complemented
45	#1728	—	13	6	no	—
46	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
47	C₂²×D₁₃	—	2	4	no	—
48	C₂²×D₁₃	#117	1	6	yes	—
49	C₂×C₄×C₁₃	—	2	6	no	—
50	C₂×C₄×C₁₃	—	2	12	no	—
51	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
52	C₂×Dic₁₃	—	2	6	no	—
53	C₂×Dic₁₃	—	2	12	no	—
54	C₂×Dic₁₃	#117	1	6	yes	—
55	C₄×D₁₃	—	4	24	no	—
56	C₄×D₁₃	#126	1	16	yes	—
57	C₈×C₁₃	—	4	4	no	—
58	#1055	—	4	4	no	—
59	C₂²×M₁₆	—	13	4	no	—
60	C₂²×C₄²	—	13	3	no	—
61	#376	—	13	3	no	—
62	#376	—	13	4	no	—
63	#376	C₂×D₁₃	1	1	yes	characteristic
64	C₂×#95	—	13	4	no	—
65	#336	—	13	12	no	—
66	#336	—	13	6	no	—
67	#336	C₂×D₁₃	1	6	yes	—
68	C₂²×C₁₃	C₂×#117	1	3	yes	—
69	C₂²×C₁₃	#568	1	4	yes	—
70	C₂×D₁₃	—	2	12	no	—
71	C₂×D₁₃	#383	1	4	yes	—
72	C₄×C₁₃	—	4	6	no	—
73	C₄×C₁₃	C₂×#126	1	4	yes	—
74	Dic₁₃	—	4	6	no	—
75	Dic₁₃	#383	1	4	yes	—
76	C₂³×C₄	—	13	1	no	—
77	C₂³×C₄	—	13	6	no	—
78	C₂×M₁₆	—	26	24	no	—
79	C₂²×C₈	—	13	4	no	—
80	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
81	C₂×C₄²	—	13	6	no	—
82	C₂×C₄²	—	13	3	no	—
83	C₂×C₄²	—	26	12	no	—
84	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
85	#95	—	13	12	no	—
86	#95	C₄×D₁₃	1	4	yes	—
87	C₂×C₁₃	C₂×#383	1	1	yes	characteristic
88	C₂×C₁₃	#2921	1	6	yes	—
89	D₁₃	—	2	4	no	—
90	C₂⁴	—	13	1	no	—
91	C₂²×C₄	—	13	1	no	—
92	C₂²×C₄	—	13	12	no	—
93	C₂²×C₄	—	13	6	no	—
94	C₂²×C₄	—	26	12	no	—
95	C₂²×C₄	—	52	12	no	—
96	C₂²×C₄	C₂×C₄×D₁₃	1	6	yes	—
97	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
98	M₁₆	—	52	16	no	—
99	C₂×C₈	—	2	12	no	—
100	C₂×C₈	—	26	12	no	—
101	C₄²	—	2	6	no	—
102	C₄²	—	26	12	no	—
103	C₄²	—	26	6	no	—
104	C₁₃	#20773	1	1	yes	characteristic, complemented, Sylow
105	C₂³	—	13	6	no	—
106	C₂³	—	26	4	no	—
107	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
108	C₂×C₄	—	2	12	no	—
109	C₂×C₄	—	2	6	no	—
110	C₂×C₄	—	13	6	no	—
111	C₂×C₄	—	13	16	no	—
112	C₂×C₄	—	26	12	no	—
113	C₂×C₄	—	26	6	no	—
114	C₂×C₄	—	52	24	no	—
115	C₂×C₄	#41×D₁₃	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	52	4	no	—
118	C₂²	—	13	4	no	—
119	C₂²	—	26	12	no	—
120	C₂²	D₁₃×#117	1	3	yes	—
121	C₂²	#11719455	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	13	4	no	—
124	C₄	—	52	6	no	—
125	C₄	D₁₃×#126	1	4	yes	—
126	C₂	—	26	4	no	—
127	C₂	D₁₃×#383	1	1	yes	characteristic
128	C₂	#13123470	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₃×#376

C₂

yes

maximal, characteristic

#13114981

C₂

yes

maximal, characteristic, complemented

#13114980

C₂

yes

maximal, complemented

#13114528

C₂

yes

maximal

C₁₃×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×#6094

C₂²

yes

—

C₂×C₄²×D₁₃

C₂²

yes

—

C₁₃×#376

C₂²

yes

characteristic

#11718593

C₂²

yes

—

D₁₃×#95

C₄

yes

—

#11718309

C₄

yes

—

C₁₃×#336

C₂²

yes

—

#11718142

C₂²

yes

—

#11718116

C₂²

yes

—

C₂²×C₄×D₁₃

C₂×C₄

yes

—

C₂²×C₄×D₁₃

C₂³

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

—

C₂×C₄²×C₁₃

C₂³

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂³

yes

—

C₂²×#1055

C₂³

yes

—

C₂×#6094

—

C₄²×D₁₃

—

C₁₃×#95

C₂×C₄

yes

—

#88071

C₂×C₄

yes

—

#20773

—

maximal, Sylow

C₂³×D₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂⁴

yes

characteristic

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

#41

yes

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

—

—

—

—

—

D₁₃

yes

characteristic, complemented

#1728

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

#117

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#117

yes

—

C₄×D₁₃

—

C₄×D₁₃

#126

yes

—

C₈×C₁₃

—

#1055

—

C₂²×M₁₆

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₁₃

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₁₃

yes

—

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

#568

yes

—

C₂×D₁₃

—

C₂×D₁₃

#383

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×#126

yes

—

Dic₁₃

—

Dic₁₃

#383

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

C₂²×D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₃

yes

—

#95

—

#95

C₄×D₁₃

yes

—

C₂×C₁₃

C₂×#383

yes

characteristic

C₂×C₁₃

#2921

yes

—

D₁₃

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₁₃

yes

—

C₂²×C₄

C₂³×D₁₃

yes

characteristic

M₁₆

—

C₂×C₈

—

100

C₂×C₈

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₁₃

#20773

yes

characteristic, complemented, Sylow

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₁₃

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

#41×D₁₃

yes

—

116

C₈

—

117

C₈

—

118

C₂²

—

119

C₂²

—

120

C₂²

D₁₃×#117

yes

—

121

C₂²

#11719455

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

D₁₃×#126

yes

—

126

C₂

—

127

C₂

D₁₃×#383

yes

characteristic

128

C₂

#13123470

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1840	C₂
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1840	D₁₃
hypocenter	C₁₃	#20773
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₁₃

commutator, socle

C₂³×C₁₃

C₂³×C₄

Fitting

C₁₃×#1840

C₂

prime radical

C₂³×D₁₃

C₂²×C₄

cosocle

C₂²×C₄×C₁₃

C₂⁴

D₁₃

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #13114981	C₂	semidirect
3. #13114980	C₂	semidirect
5. C₁₃×#1840	C₂	semidirect
44. #1840	D₁₃	semidirect
104. C₁₃	#20773	semidirect

H ≅ G/N

type

2. #13114981

C₂

semidirect

3. #13114980

C₂

semidirect

5. C₁₃×#1840

C₂

semidirect

44. #1840

D₁₃

semidirect

104. C₁₃

#20773

semidirect

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

subgroup	index
D₁₃×#376	2
#13114981	2
#13114980	2
#13114528	2
C₁₃×#1840	2
#20773	13

subgroup

index

D₁₃×#376

C₁₃×#1840

Subgroups — #15863170

Conjugacy classes of subgroups

Complements

Maximal subgroups