Group #14298920 — subgroups

Subgroups — C₃×#10600634 #14298920

Order 1920.

360 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 186 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×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic
2	C₃×#65213	C₂	1	2	yes	maximal
3	C₃×#64772	C₂	1	4	yes	maximal
4	#10600634	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×#681	C₂²	1	4	yes	—
8	C₃×C₅×#97	C₄	1	4	yes	—
9	C₃×C₄⋊#168	—	2	4	no	—
10	C₃×#1838	—	5	1	no	maximal, Hall
11	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic
12	#65213	C₂×C₃	1	2	yes	—
13	#64772	C₂×C₃	1	4	yes	—
14	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
15	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
16	C₂×C₃×C₅×C₈	—	2	4	no	—
17	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
18	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
19	C₃×C₄²×C₅	D₄	1	2	yes	—
20	C₃×#681	—	2	8	no	—
21	C₂×C₃×#168	—	2	4	no	—
22	C₃×#423	—	5	2	no	—
23	C₂×C₃×#97	D₅	1	1	yes	characteristic
24	C₃×#341	—	5	4	no	—
25	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
26	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
27	C₂×#681	C₂²×C₃	1	4	yes	—
28	C₅×#97	C₃×C₄	1	4	yes	—
29	C₄⋊#168	—	2	4	no	—
30	#1838	—	5	1	no	Sylow
31	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	—	4	2	no	—
33	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
34	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₅	#41	1	4	yes	—
37	C₃×C₅×C₈	—	2	4	no	—
38	C₃×#168	—	4	4	no	—
39	C₂×C₃×M₁₆	—	5	4	no	—
40	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
41	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
42	C₃×C₄⋊C₈	—	10	4	no	—
43	C₃×#97	Dic₅	1	4	yes	—
44	C₂²×C₄×C₅	C₃×Q₈	1	2	yes	—
45	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
46	C₂×C₅×C₈	—	2	4	no	—
47	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
48	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
49	C₄²×C₅	C₃×D₄	1	2	yes	—
50	#681	—	2	8	no	—
51	C₂×#168	—	2	4	no	—
52	#423	—	5	2	no	—
53	C₂×#97	C₃×D₅	1	1	yes	characteristic
54	#341	—	5	4	no	—
55	C₂²×C₃×C₅	—	2	2	no	—
56	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₃×C₅	#125	1	2	yes	—
58	C₃×C₄×C₅	—	2	4	no	—
59	C₃×C₄×C₅	#117	1	2	yes	—
60	C₃×C₄×C₅	#124	1	2	yes	—
61	C₂²×C₃×C₄	Dic₁₀	1	2	yes	—
62	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
63	C₃×M₁₆	—	10	8	no	—
64	C₂×C₃×C₈	—	2	4	no	—
65	C₂×C₃×C₈	—	10	4	no	—
66	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	—
67	C₃×C₄²	D₂₀	1	2	yes	—
68	C₃×C₄²	C₂×Dic₅	1	2	yes	—
69	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₅	—	4	2	no	—
71	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
72	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
73	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
74	C₂×C₄×C₅	C₃×#41	1	4	yes	—
75	C₅×C₈	—	2	4	no	—
76	#168	—	4	4	no	—
77	C₂×M₁₆	—	5	4	no	—
78	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
79	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
80	C₄⋊C₈	—	10	4	no	—
81	#97	C₃×Dic₅	1	4	yes	—
82	C₂×C₃×C₅	—	2	2	no	—
83	C₂×C₃×C₅	#382	1	1	yes	characteristic
84	C₂×C₃×C₅	#430	1	2	yes	—
85	C₂³×C₃	C₂×Dic₁₀	1	1	yes	characteristic
86	C₂×C₃×C₄	—	4	2	no	—
87	C₂×C₃×C₄	C₄⋊Dic₅	1	4	yes	—
88	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
89	C₂×C₃×C₄	#709	1	4	yes	—
90	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
91	C₃×C₈	—	2	4	no	—
92	C₃×C₈	—	20	4	no	—
93	C₂²×C₅	—	2	2	no	—
94	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₅	C₃×#125	1	2	yes	—
96	C₄×C₅	—	2	4	no	—
97	C₄×C₅	C₃×#117	1	2	yes	—
98	C₄×C₅	C₃×#124	1	2	yes	—
99	C₂²×C₄	C₃×Dic₁₀	1	2	yes	—
100	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
101	M₁₆	—	10	8	no	—
102	C₂×C₈	—	2	4	no	—
103	C₂×C₈	—	10	4	no	—
104	C₂×C₈	C₂×C₃×Dic₅	1	4	yes	—
105	C₄²	C₃×D₂₀	1	2	yes	—
106	C₄²	C₂×C₃×Dic₅	1	2	yes	—
107	C₃×C₅	#1838	1	1	yes	characteristic, complemented, Hall
108	C₂²×C₃	—	2	2	no	—
109	C₂²×C₃	#4016	1	2	yes	—
110	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
111	C₃×C₄	—	2	4	no	—
112	C₃×C₄	#4021	1	2	yes	—
113	C₃×C₄	#4072	1	2	yes	—
114	C₂×C₅	—	2	2	no	—
115	C₂×C₅	C₃×#382	1	1	yes	characteristic
116	C₂×C₅	C₃×#430	1	2	yes	—
117	C₂³	C₂×C₃×Dic₁₀	1	1	yes	characteristic
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	C₃×C₄⋊Dic₅	1	4	yes	—
120	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
121	C₂×C₄	C₃×#709	1	4	yes	—
122	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
123	C₈	—	2	4	no	—
124	C₈	—	20	4	no	—
125	C₂×C₃	—	2	2	no	—
126	C₂×C₃	#65225	1	1	yes	characteristic
127	C₂×C₃	#65414	1	2	yes	—
128	C₅	C₃×#1838	1	1	yes	characteristic, complemented, Sylow
129	C₂²	—	2	2	no	—
130	C₂²	C₃×#4016	1	2	yes	—
131	C₂²	C₂×C₃×C₄⋊Dic₅	1	1	yes	characteristic
132	C₄	—	2	4	no	—
133	C₄	C₃×#4021	1	2	yes	—
134	C₄	C₃×#4072	1	2	yes	—
135	C₃	#10600634	1	1	yes	characteristic, direct product factor, Sylow
136	C₂	—	2	2	no	—
137	C₂	C₃×#65225	1	1	yes	characteristic
138	C₂	C₃×#65414	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅×#97

C₂

yes

maximal, characteristic

C₃×#65213

C₂

yes

maximal

C₃×#64772

C₂

yes

maximal

#10600634

C₃

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₃×C₅×C₈

C₂²

yes

—

C₂×C₃×C₄²×C₅

C₂²

yes

characteristic

C₂×C₃×#681

C₂²

yes

—

C₃×C₅×#97

C₄

yes

—

C₃×C₄⋊#168

—

C₃×#1838

—

maximal, Hall

C₂×C₅×#97

C₂×C₃

yes

characteristic

#65213

C₂×C₃

yes

—

#64772

C₂×C₃

yes

—

C₂²×C₃×C₄×C₅

Q₈

yes

—

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

C₂×C₃×C₅×C₈

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

—

C₃×C₄²×C₅

C₂×C₄

yes

—

C₃×C₄²×C₅

D₄

yes

—

C₃×#681

—

C₂×C₃×#168

—

C₃×#423

—

C₂×C₃×#97

D₅

yes

characteristic

C₃×#341

—

C₂²×C₅×C₈

C₂²×C₃

yes

—

C₂×C₄²×C₅

C₂²×C₃

yes

characteristic

C₂×#681

C₂²×C₃

yes

—

C₅×#97

C₃×C₄

yes

—

C₄⋊#168

—

#1838

—

Sylow

C₂³×C₃×C₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₃×C₅×C₈

—

C₃×#168

—

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

C₂×D₅

yes

—

C₂×C₃×C₄²

C₂×D₅

yes

characteristic

C₃×C₄⋊C₈

—

C₃×#97

Dic₅

yes

—

C₂²×C₄×C₅

C₃×Q₈

yes

—

C₂²×C₄×C₅

C₂³×C₃

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂×C₃×C₄

yes

—

C₄²×C₅

C₂×C₃×C₄

yes

—

C₄²×C₅

C₃×D₄

yes

—

#681

—

C₂×#168

—

#423

—

C₂×#97

C₃×D₅

yes

characteristic

#341

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃×C₅

#125

yes

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#117

yes

—

C₃×C₄×C₅

#124

yes

—

C₂²×C₃×C₄

Dic₁₀

yes

—

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

C₃×M₁₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×Dic₅

yes

—

C₃×C₄²

D₂₀

yes

—

C₃×C₄²

C₂×Dic₅

yes

—

C₂³×C₅

C₂×C₃×Q₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₃×C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂²×C₃×C₄

yes

characteristic

C₂×C₄×C₅

C₂×C₃×D₄

yes

characteristic

C₂×C₄×C₅

C₃×#41

yes

—

C₅×C₈

—

#168

—

C₂×M₁₆

—

C₂²×C₈

C₂×C₃×D₅

yes

—

C₂×C₄²

C₂×C₃×D₅

yes

characteristic

C₄⋊C₈

—

#97

C₃×Dic₅

yes

—

C₂×C₃×C₅

—

C₂×C₃×C₅

#382

yes

characteristic

C₂×C₃×C₅

#430

yes

—

C₂³×C₃

C₂×Dic₁₀

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₅

yes

—

C₂×C₃×C₄

C₂×D₂₀

yes

characteristic

C₂×C₃×C₄

#709

yes

—

C₂×C₃×C₄

C₂²×Dic₅

yes

characteristic

C₃×C₈

—

C₃×C₈

—

C₂²×C₅

—

C₂²×C₅

C₂×C₃×C₄⋊C₄

yes

characteristic

C₂²×C₅

C₃×#125

yes

—

C₄×C₅

—

C₄×C₅

C₃×#117

yes

—

C₄×C₅

C₃×#124

yes

—

C₂²×C₄

C₃×Dic₁₀

yes

—

100

C₂²×C₄

C₂²×C₃×D₅

yes

characteristic

101

M₁₆

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂×C₃×Dic₅

yes

—

105

C₄²

C₃×D₂₀

yes

—

106

C₄²

C₂×C₃×Dic₅

yes

—

107

C₃×C₅

#1838

yes

characteristic, complemented, Hall

108

C₂²×C₃

—

109

C₂²×C₃

#4016

yes

—

110

C₂²×C₃

C₂×C₄⋊Dic₅

yes

characteristic

111

C₃×C₄

—

112

C₃×C₄

#4021

yes

—

113

C₃×C₄

#4072

yes

—

114

C₂×C₅

—

115

C₂×C₅

C₃×#382

yes

characteristic

116

C₂×C₅

C₃×#430

yes

—

117

C₂³

C₂×C₃×Dic₁₀

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

C₃×C₄⋊Dic₅

yes

—

120

C₂×C₄

C₂×C₃×D₂₀

yes

characteristic

121

C₂×C₄

C₃×#709

yes

—

122

C₂×C₄

C₂²×C₃×Dic₅

yes

characteristic

123

C₈

—

124

C₈

—

125

C₂×C₃

—

126

C₂×C₃

#65225

yes

characteristic

127

C₂×C₃

#65414

yes

—

128

C₅

C₃×#1838

yes

characteristic, complemented, Sylow

129

C₂²

—

130

C₂²

C₃×#4016

yes

—

131

C₂²

C₂×C₃×C₄⋊Dic₅

yes

characteristic

132

C₄

—

133

C₄

C₃×#4021

yes

—

134

C₄

C₃×#4072

yes

—

135

C₃

#10600634

yes

characteristic, direct product factor, Sylow

136

C₂

—

137

C₂

C₃×#65225

yes

characteristic

138

C₂

C₃×#65414

yes

—

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×C₅	C₂×Q₈
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#97	D₅
hypocenter	C₅	C₃×#1838
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

subgroup

G/H

center

C₂×C₃×C₄

C₂×D₂₀

commutator

C₂×C₄×C₅

C₂²×C₃×C₄

Frattini

C₂²×C₄

C₂²×C₃×D₅

Fitting

C₂×C₃×C₅×#97

C₂

socle

C₂²×C₃×C₅

C₂×C₄⋊C₄

prime radical

C₂³×C₃×C₅

C₂×Q₈

cosocle

C₂²×C₄×C₅

C₂³×C₃

hypercenter

C₂×C₃×#97

D₅

hypocenter

C₅

C₃×#1838

LCS

G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

N	H ≅ G/N	type
4. #10600634	C₃	direct (N × H)
107. C₃×C₅	#1838	semidirect
128. C₅	C₃×#1838	semidirect
135. C₃	#10600634	direct (N × H)

H ≅ G/N

type

4. #10600634

C₃

direct (N × H)

107. C₃×C₅

#1838

semidirect

128. C₅

C₃×#1838

semidirect

135. C₃

#10600634

direct (N × H)

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

subgroup	index
C₂×C₃×C₅×#97	2
C₃×#65213	2
C₃×#64772	2
#10600634	3
C₃×#1838	5

subgroup

index

C₂×C₃×C₅×#97

Subgroups — C₃×#10600634 #14298920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10600634 #14298920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600634 #14298920