Group #15752233 — subgroups

Subgroups — #15752233

Order 3328.

322 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 83 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	#13116399	C₂	1	3	yes	maximal
2	#13112659	C₂	1	3	yes	maximal
3	C₁₃×#2810	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#400	—	2	3	no	—
5	C₁₃×#389	C₂²	1	3	yes	—
6	C₁₃×#387	—	2	3	no	—
7	#11718596	C₂²	1	1	yes	characteristic
8	#11718121	—	2	3	no	—
9	#11718121	—	2	3	no	—
10	#11718116	C₂²	1	3	yes	—
11	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
12	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
13	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
14	C₂×C₄²×C₁₃	—	2	1	no	—
15	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₃	—	2	3	no	—
17	C₂²×#1055	—	2	3	no	—
18	C₁₃×#95	—	2	3	no	—
19	C₁₃×#95	—	2	3	no	—
20	C₁₃×#95	—	2	1	no	—
21	C₁₃×#95	—	2	3	no	—
22	#7832	—	13	1	no	maximal, Sylow
23	C₂²×C₄×C₁₃	—	2	3	no	—
24	C₂²×C₄×C₁₃	—	2	3	no	—
25	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
26	C₂²×Dic₁₃	—	4	1	no	—
27	C₁₃×C₄⋊C₄	—	2	3	no	—
28	C₁₃×C₄⋊C₄	—	2	3	no	—
29	C₁₃×C₄⋊C₄	—	4	3	no	—
30	C₁₃×C₄⋊C₄	—	4	3	no	—
31	C₁₃×C₄⋊C₄	—	4	3	no	—
32	C₄²×C₁₃	—	4	1	no	—
33	C₄²×C₁₃	—	8	1	no	—
34	C₄⋊Dic₁₃	—	4	6	no	—
35	C₂×#1055	—	4	3	no	—
36	C₂×#1055	—	4	3	no	—
37	C₂×#1055	—	4	3	no	—
38	#2810	D₁₃	1	1	yes	characteristic
39	#2100	—	13	3	no	—
40	#1271	—	13	3	no	—
41	C₂³×C₁₃	#120	1	1	yes	characteristic
42	C₂×C₄×C₁₃	—	2	3	no	—
43	C₂×C₄×C₁₃	—	2	3	no	—
44	C₂×C₄×C₁₃	—	4	3	no	—
45	C₂×C₄×C₁₃	—	4	3	no	—
46	C₂×C₄×C₁₃	—	4	3	no	—
47	C₂×C₄×C₁₃	—	4	3	no	—
48	C₂×C₄×C₁₃	—	4	3	no	—
49	C₂×C₄×C₁₃	—	4	3	no	—
50	C₂×C₄×C₁₃	#135	1	3	yes	—
51	C₂×C₄×C₁₃	#137	1	3	yes	—
52	C₂×Dic₁₃	—	8	3	no	—
53	#1055	—	8	3	no	—
54	#400	—	2	3	no	—
55	#389	C₂×D₁₃	1	3	yes	—
56	#387	—	2	3	no	—
57	#384	—	13	1	no	—
58	#340	—	26	3	no	—
59	#340	—	26	3	no	—
60	#336	—	13	3	no	—
61	C₂²×C₁₃	#452	1	3	yes	—
62	C₂²×C₁₃	#454	1	3	yes	—
63	C₂²×C₁₃	#458	1	1	yes	characteristic
64	C₄×C₁₃	—	2	3	no	—
65	C₄×C₁₃	—	2	3	no	—
66	C₄×C₁₃	—	8	3	no	—
67	C₄×C₁₃	—	8	3	no	—
68	Dic₁₃	—	16	1	no	—
69	C₂²×C₈	—	26	3	no	—
70	C₂×C₄⋊C₄	—	2	3	no	—
71	C₂×C₄⋊C₄	—	26	3	no	—
72	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	3	yes	—
73	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	3	yes	—
74	C₂×C₄²	—	2	1	no	—
75	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
76	#95	—	2	3	no	—
77	#95	—	2	3	no	—
78	#95	—	2	1	no	—
79	#95	—	2	3	no	—
80	C₂×C₁₃	#1615	1	3	yes	—
81	C₂×C₁₃	#1638	1	3	yes	—
82	C₂×C₁₃	#1658	1	1	yes	characteristic
83	C₂²×C₄	—	2	3	no	—
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	52	1	no	—
86	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
87	C₂×C₈	—	52	3	no	—
88	C₂×C₈	—	52	3	no	—
89	C₂×C₈	—	52	3	no	—
90	C₄⋊C₄	—	2	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	4	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	52	6	no	—
96	C₄²	—	4	1	no	—
97	C₄²	—	8	1	no	—
98	C₁₃	#7832	1	1	yes	characteristic, complemented, Sylow
99	C₂³	#88207	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	104	3	no	—
109	C₂×C₄	#88204	1	3	yes	—
110	C₂×C₄	#88205	1	3	yes	—
111	C₈	—	104	3	no	—
112	C₂²	#11718900	1	3	yes	—
113	C₂²	#11718904	1	1	yes	characteristic
114	C₂²	#11718906	1	3	yes	—
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	208	1	no	—
120	C₂	#13113867	1	3	yes	—
121	C₂	#13114008	1	3	yes	—
122	C₂	#13114138	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13116399

C₂

yes

maximal

#13112659

C₂

yes

maximal

C₁₃×#2810

C₂

yes

maximal, characteristic

C₁₃×#400

—

C₁₃×#389

C₂²

yes

—

C₁₃×#387

—

#11718596

C₂²

yes

—

—

C₂²

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#7832

—

maximal, Sylow

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

—

—

—

D₁₃

yes

characteristic

#2100

—

#1271

—

C₂³×C₁₃

#120

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#135

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

#1055

—

#400

—

#389

C₂×D₁₃

yes

—

—

—

—

—

—

C₂²×C₁₃

#452

yes

—

C₂²×C₁₃

#454

yes

—

C₂²×C₁₃

#458

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

C₂×C₄⋊C₄

C₂²⋊D₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₃

yes

—

—

—

—

C₂×C₁₃

#1615

yes

—

C₂×C₁₃

#1638

yes

—

C₂×C₁₃

#1658

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₁₃

#7832

yes

characteristic, complemented, Sylow

C₂³

#88207

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

104

—

109

C₂×C₄

#88204

yes

—

110

C₂×C₄

#88205

yes

—

111

C₈

—

104

—

112

C₂²

#11718900

yes

—

113

C₂²

#11718904

yes

characteristic

114

C₂²

#11718906

yes

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

208

—

120

C₂

#13113867

yes

—

121

C₂

#13114008

yes

—

122

C₂

#13114138

yes

characteristic

	subgroup	G/H
center	C₂³	#88207
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2810	C₂
socle, prime radical	C₂³×C₁₃	#120
hypercenter	#2810	D₁₃
hypocenter	C₁₃	#7832
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

subgroup

G/H

center

C₂³

#88207

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2810

C₂

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂³×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

N	H ≅ G/N	type
98. C₁₃	#7832	semidirect

H ≅ G/N

type

98. C₁₃

#7832

semidirect

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

subgroup	index
#13116399	2
#13112659	2
C₁₃×#2810	2
#7832	13

subgroup

index

#13116399

#13112659

C₁₃×#2810

#7832

Subgroups — #15752233

Conjugacy classes of subgroups

Complements

Maximal subgroups