Group #15750100 — subgroups

Subgroups — #15750100

Order 3328.

208 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11718055	C₂	1	2	yes	maximal
2	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#108	—	2	2	no	—
4	C₁₃×#423	C₄	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88052	—	2	2	no	—
7	#11718055	—	2	2	no	—
8	#11718055	C₄	1	4	yes	—
9	C₂×C₁₃×M₁₆	—	2	2	no	—
10	C₂²×C₈×C₁₃	D₄	1	2	yes	—
11	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₁₃×#108	—	4	2	no	—
13	C₁₃×#108	—	4	2	no	—
14	C₁₃×C₄⋊C₈	—	4	2	no	—
15	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
18	#88052	—	2	4	no	—
19	#88052	—	4	2	no	—
20	C₂×#6090	—	4	2	no	—
21	#7272	—	13	1	no	maximal, Sylow
22	C₂²×C₄×C₁₃	—	2	1	no	—
23	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₃×M₁₆	—	4	4	no	—
25	C₂×C₈×C₁₃	—	4	2	no	—
26	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₃	D₈	1	2	yes	—
29	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
30	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
31	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
32	C₄²×C₁₃	—	2	1	no	—
33	C₄²×C₁₃	C₄²	1	1	yes	characteristic
34	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	#6090	—	4	4	no	—
36	C₂×#364	—	13	2	no	—
37	#1848	D₁₃	1	1	yes	characteristic
38	C₂³×C₁₃	#101	1	1	yes	characteristic
39	C₂×C₄×C₁₃	—	2	1	no	—
40	C₂×C₄×C₁₃	—	2	1	no	—
41	C₂×C₄×C₁₃	—	4	2	no	—
42	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
43	C₂×C₄×C₁₃	#100	1	1	yes	characteristic
44	C₂×C₄×C₁₃	#102	1	2	yes	—
45	C₂×C₄×C₁₃	#103	1	2	yes	—
46	C₈×C₁₃	—	8	2	no	—
47	C₈×C₁₃	#102	1	2	yes	—
48	C₈×C₁₃	#103	1	2	yes	—
49	C₈×C₁₃	#106	1	2	yes	—
50	C₈×C₁₃	#107	1	2	yes	—
51	C₂×M₃₂	—	26	2	no	—
52	C₂×#108	—	2	2	no	—
53	#423	Dic₁₃	1	2	yes	—
54	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
55	#364	—	13	4	no	—
56	#364	—	26	2	no	—
57	C₂²×C₁₃	—	4	1	no	—
58	C₂²×C₁₃	#332	1	2	yes	—
59	C₂²×C₁₃	#343	1	1	yes	characteristic
60	C₄×C₁₃	—	2	2	no	—
61	C₄×C₁₃	—	4	1	no	—
62	C₄×C₁₃	#331	1	1	yes	characteristic
63	C₄×C₁₃	#333	1	1	yes	characteristic
64	C₄×C₁₃	#340	1	2	yes	—
65	C₂×M₁₆	—	2	2	no	—
66	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
67	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
68	M₃₂	—	26	4	no	—
69	M₃₂	—	52	2	no	—
70	C₂×C₁₆	—	52	2	no	—
71	#108	—	4	2	no	—
72	#108	—	4	2	no	—
73	C₄⋊C₈	—	4	2	no	—
74	C₄×C₈	Dic₂₆	1	1	yes	characteristic
75	C₄×C₈	C₄×D₁₃	1	2	yes	—
76	C₄×C₈	D₅₂	1	1	yes	characteristic
77	C₂×C₁₃	—	2	1	no	—
78	C₂×C₁₃	—	2	2	no	—
79	C₂×C₁₃	#1296	1	1	yes	characteristic
80	C₂²×C₄	—	2	1	no	—
81	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
82	M₁₆	—	4	4	no	—
83	C₂×C₈	—	4	2	no	—
84	C₂×C₈	#6101	1	2	yes	—
85	C₂×C₈	#6103	1	2	yes	—
86	C₂×C₈	#6104	1	2	yes	—
87	C₂×C₈	#6105	1	2	yes	—
88	C₂×C₈	#6106	1	2	yes	—
89	C₂×C₈	#6107	1	2	yes	—
90	C₄²	—	2	1	no	—
91	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
92	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
93	C₁₆	—	52	4	no	—
94	C₁₃	#7272	1	1	yes	characteristic, complemented, Sylow
95	C₂³	#88076	1	1	yes	characteristic
96	C₂×C₄	—	2	1	no	—
97	C₂×C₄	—	2	1	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	#88071	1	1	yes	characteristic
100	C₂×C₄	#88072	1	2	yes	—
101	C₂×C₄	#88073	1	1	yes	characteristic
102	C₂×C₄	#88075	1	2	yes	—
103	C₈	—	8	2	no	—
104	C₈	#88047	1	2	yes	—
105	C₈	#88048	1	2	yes	—
106	C₈	#88049	1	2	yes	—
107	C₈	#88050	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	#11718122	1	1	yes	characteristic
110	C₂²	#11718139	1	2	yes	—
111	C₄	—	2	2	no	—
112	C₄	—	4	1	no	—
113	C₄	#11718121	1	2	yes	—
114	C₄	#11718136	1	1	yes	characteristic
115	C₄	#11718138	1	1	yes	characteristic
116	C₂	—	2	1	no	—
117	C₂	—	2	2	no	—
118	C₂	#13112719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11718055

C₂

yes

maximal

C₁₃×#1848

C₂

yes

maximal, characteristic

C₂×C₁₃×#108

—

C₁₃×#423

C₄

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

—

—

C₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₁₃×#108

—

C₁₃×#108

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

D₄

yes

characteristic

C₄×C₈×C₁₃

Q₈

yes

—

—

—

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

D₈

yes

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

Q₁₆

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

C₄²

yes

characteristic

C₄²×C₁₃

C₄⋊C₄

yes

—

—

D₁₃

yes

characteristic

C₂³×C₁₃

#101

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#103

yes

—

C₈×C₁₃

—

C₈×C₁₃

#102

yes

—

C₈×C₁₃

#103

yes

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#107

yes

—

C₂×M₃₂

—

C₂×#108

—

#423

Dic₁₃

yes

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#364

—

#364

—

C₂²×C₁₃

—

C₂²×C₁₃

#332

yes

—

C₂²×C₁₃

#343

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂×M₁₆

—

C₂²×C₈

C₂²⋊D₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

Dic₂₆

yes

characteristic

C₄×C₈

C₄×D₁₃

yes

—

C₄×C₈

D₅₂

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#1296

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

#6101

yes

—

C₂×C₈

#6103

yes

—

C₂×C₈

#6104

yes

—

C₂×C₈

#6105

yes

—

C₂×C₈

#6106

yes

—

C₂×C₈

#6107

yes

—

C₄²

—

C₄²

C₄×Dic₁₃

yes

characteristic

C₄²

C₄⋊Dic₁₃

yes

characteristic

C₁₆

—

C₁₃

#7272

yes

characteristic, complemented, Sylow

C₂³

#88076

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#88071

yes

characteristic

100

C₂×C₄

#88072

yes

—

101

C₂×C₄

#88073

yes

characteristic

102

C₂×C₄

#88075

yes

—

103

C₈

—

104

C₈

#88047

yes

—

105

C₈

#88048

yes

—

106

C₈

#88049

yes

—

107

C₈

#88050

yes

—

108

C₂²

—

109

C₂²

#11718122

yes

characteristic

110

C₂²

#11718139

yes

—

111

C₄

—

112

C₄

—

113

C₄

#11718121

yes

—

114

C₄

#11718136

yes

characteristic

115

C₄

#11718138

yes

characteristic

116

C₂

—

117

C₂

—

118

C₂

#13112719

yes

characteristic

	subgroup	G/H
center	C₄	#11718138
commutator	C₄²×C₁₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₃
Fitting	C₁₃×#1848	C₂
socle	C₂×C₁₃	#1296
prime radical	C₂³×C₁₃	#101
cosocle	C₂×C₄×C₈×C₁₃	C₂²
hypercenter	#1848	D₁₃
hypocenter	C₁₃	#7272
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

subgroup

G/H

center

C₄

#11718138

commutator

C₄²×C₁₃

C₄²

Frattini

C₂×C₄×C₈

C₂×D₁₃

Fitting

C₁₃×#1848

C₂

C₂×C₁₃

C₂³×C₁₃

C₂×C₄×C₈×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1848

N	H ≅ G/N	type
94. C₁₃	#7272	semidirect

H ≅ G/N

type

94. C₁₃

#7272

semidirect

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

subgroup	index
C₂×#11718055	2
C₁₃×#1848	2
#7272	13

subgroup

index

C₂×#11718055

C₁₃×#1848

#7272

Subgroups — #15750100

Conjugacy classes of subgroups

Complements

Maximal subgroups