Group #14563525 — subgroups

Subgroups — C₄×#10597265 #14563525

Order 2432.

280 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10597265	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926306	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₉	—	2	1	no	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₉	—	2	1	no	—
11	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×#95	—	2	1	no	—
14	C₁₉⋊#95	—	2	1	no	—
15	#10597265	C₄	1	8	yes	direct product factor
16	C₄×C₁₉⋊C₈	C₄	1	4	yes	complemented
17	C₂²×C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
24	C₄²×C₁₉	—	4	2	no	—
25	C₄²×C₁₉	C₂×C₄	1	2	yes	—
26	C₄²×C₁₉	Q₈	1	2	yes	—
27	C₄⋊Dic₁₉	—	2	2	no	—
28	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	—
29	C₄×Dic₁₉	—	4	2	no	—
30	C₂×C₁₉⋊C₈	—	2	2	no	—
31	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
33	C₂×C₁₉⋊C₈	C₂×C₄	1	4	yes	—
34	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	—	4	2	no	—
39	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
41	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
42	C₂×C₄×C₁₉	SD₁₆	1	2	yes	—
43	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	2	yes	—
47	C₂×Dic₁₉	—	2	4	no	—
48	C₂×Dic₁₉	—	4	2	no	—
49	C₂×Dic₁₉	—	4	2	no	—
50	C₁₉⋊C₈	—	2	2	no	—
51	C₁₉⋊C₈	C₄²	1	4	yes	complemented
52	C₄×#106	—	19	1	no	maximal, Sylow
53	C₂²×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₁₉	C₄×D₄	1	2	yes	—
55	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
56	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
57	C₂²×C₁₉	#135	1	2	yes	—
58	C₄×C₁₉	—	2	2	no	—
59	C₄×C₁₉	—	4	4	no	—
60	C₄×C₁₉	#106	1	4	yes	complemented
61	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
62	C₄×C₁₉	#117	1	1	yes	characteristic
63	C₄×C₁₉	C₄×Q₈	1	2	yes	—
64	Dic₁₉	—	4	4	no	—
65	C₂×#106	—	19	2	no	—
66	C₂×C₄×C₈	—	19	1	no	—
67	C₄×C₄⋊C₄	—	19	1	no	—
68	C₄×C₄⋊C₄	D₁₉	1	1	yes	characteristic
69	#340	—	19	2	no	—
70	C₂×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₁₉	C₂×#106	1	1	yes	characteristic
72	C₂×C₁₉	#427	1	1	yes	characteristic
73	C₂×C₁₉	C₄×SD₁₆	1	2	yes	—
74	C₂×C₁₉	C₄×SD₁₆	1	2	yes	—
75	C₂²×C₈	—	19	1	no	—
76	C₂²×C₈	—	19	1	no	—
77	C₂×C₄⋊C₄	—	19	2	no	—
78	C₂×C₄⋊C₄	C₂×D₁₉	1	2	yes	—
79	C₂×C₄²	—	2	1	no	—
80	C₂×C₄²	—	38	1	no	—
81	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
82	#106	—	19	8	no	—
83	C₄×C₈	—	19	4	no	—
84	#95	—	2	1	no	—
85	#95	—	38	1	no	—
86	C₁₉	C₄×#106	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	38	2	no	—
89	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
90	C₂²×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
91	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
92	C₂×C₈	—	19	2	no	—
93	C₂×C₈	—	19	4	no	—
94	C₂×C₈	—	19	2	no	—
95	C₂×C₈	—	38	2	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	19	4	no	—
98	C₄⋊C₄	—	38	2	no	—
99	C₄⋊C₄	C₄×D₁₉	1	4	yes	—
100	C₄²	—	4	2	no	—
101	C₄²	—	76	2	no	—
102	C₄²	Dic₃₈	1	2	yes	—
103	C₄²	C₄×D₁₉	1	2	yes	—
104	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	38	4	no	—
110	C₂×C₄	—	76	2	no	—
111	C₂×C₄	—	76	2	no	—
112	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
113	C₂×C₄	Dic₁₉⋊C₄	1	2	yes	—
114	C₂×C₄	#64526	1	2	yes	—
115	C₂×C₄	#64527	1	2	yes	—
116	C₂×C₄	C₂×Dic₃₈	1	1	yes	characteristic
117	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
118	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
119	C₂×C₄	#64541	1	2	yes	—
120	C₈	—	19	4	no	—
121	C₈	—	38	2	no	—
122	C₂²	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
123	C₂²	C₄×C₂²⋊D₁₉	1	2	yes	—
124	C₂²	C₂×#64526	1	1	yes	characteristic
125	C₂²	C₂×#64527	1	1	yes	characteristic
126	C₂²	#10597396	1	2	yes	—
127	C₄	—	2	2	no	—
128	C₄	—	4	4	no	—
129	C₄	—	76	4	no	—
130	C₄	#10597265	1	4	yes	direct product factor
131	C₄	C₄×Dic₃₈	1	2	yes	—
132	C₄	C₄²×D₁₉	1	1	yes	characteristic
133	C₄	#10597318	1	1	yes	characteristic
134	C₂	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
135	C₂	C₂×#10597265	1	1	yes	characteristic
136	C₂	#11926580	1	1	yes	characteristic
137	C₂	C₄×#64526	1	2	yes	—
138	C₂	C₄×#64527	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597265

C₂

yes

maximal

C₂×C₄×C₁₉⋊C₈

C₂

yes

maximal, characteristic

C₄×C₄⋊Dic₁₉

C₂

yes

maximal, characteristic

#11926306

C₂

yes

maximal

C₄×C₄⋊C₄×C₁₉

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₂²×C₁₉⋊C₈

C₂²

yes

characteristic

C₁₉×#95

—

C₁₉⋊#95

—

#10597265

C₄

yes

direct product factor

C₄×C₁₉⋊C₈

C₄

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₄

yes

—

C₄²×C₁₉

Q₈

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂×C₄

yes

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂×C₁₉⋊C₈

C₂×C₄

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

SD₁₆

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

C₄²

yes

complemented

C₄×#106

—

maximal, Sylow

C₂²×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂²×C₁₉

#135

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#106

yes

complemented

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

#117

yes

characteristic

C₄×C₁₉

C₄×Q₈

yes

—

Dic₁₉

—

C₂×#106

—

C₂×C₄×C₈

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

D₁₉

yes

characteristic

#340

—

C₂×C₁₉

C₄×C₄⋊C₄

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

C₄×SD₁₆

yes

—

C₂×C₁₉

C₄×SD₁₆

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#106

—

C₄×C₈

—

#95

—

#95

—

C₁₉

C₄×#106

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²⋊D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₁₉

yes

—

100

C₄²

—

101

C₄²

—

102

C₄²

Dic₃₈

yes

—

103

C₄²

C₄×D₁₉

yes

—

104

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

Dic₁₉⋊C₄

yes

—

113

C₂×C₄

Dic₁₉⋊C₄

yes

—

114

C₂×C₄

#64526

yes

—

115

C₂×C₄

#64527

yes

—

116

C₂×C₄

C₂×Dic₃₈

yes

characteristic

117

C₂×C₄

C₂×C₄×D₁₉

yes

—

118

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

119

C₂×C₄

#64541

yes

—

120

C₈

—

121

C₈

—

122

C₂²

C₂×Dic₁₉⋊C₄

yes

characteristic

123

C₂²

C₄×C₂²⋊D₁₉

yes

—

124

C₂²

C₂×#64526

yes

characteristic

125

C₂²

C₂×#64527

yes

characteristic

126

C₂²

#10597396

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#10597265

yes

direct product factor

131

C₄

C₄×Dic₃₈

yes

—

132

C₄

C₄²×D₁₉

yes

characteristic

133

C₄

#10597318

yes

characteristic

134

C₂

C₄×Dic₁₉⋊C₄

yes

characteristic

135

C₂

C₂×#10597265

yes

characteristic

136

C₂

#11926580

yes

characteristic

137

C₂

C₄×#64526

yes

—

138

C₂

C₄×#64527

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₁₉
commutator	C₄×C₁₉	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₉
Fitting	C₄×C₄⋊C₄×C₁₉	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
cosocle	C₂²×C₄×C₁₉	C₂³
hypercenter	C₄×C₄⋊C₄	D₁₉
hypocenter	C₁₉	C₄×#106
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

subgroup

G/H

center

C₂²×C₄

C₂²⋊D₁₉

commutator

C₄×C₁₉

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₁₉

Fitting

C₄×C₄⋊C₄×C₁₉

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

cosocle

C₂²×C₄×C₁₉

C₂³

hypercenter

C₄×C₄⋊C₄

D₁₉

hypocenter

C₁₉

C₄×#106

LCS

G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₄×C₄⋊C₄

N	H ≅ G/N	type
15. #10597265	C₄	direct (N × H)
16. C₄×C₁₉⋊C₈	C₄	semidirect
51. C₁₉⋊C₈	C₄²	semidirect
60. C₄×C₁₉	#106	semidirect
86. C₁₉	C₄×#106	semidirect
130. C₄	#10597265	direct (N × H)

H ≅ G/N

type

15. #10597265

C₄

direct (N × H)

16. C₄×C₁₉⋊C₈

C₄

semidirect

51. C₁₉⋊C₈

C₄²

semidirect

60. C₄×C₁₉

#106

semidirect

86. C₁₉

C₄×#106

semidirect

130. C₄

#10597265

direct (N × H)

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

subgroup	index
C₂×#10597265	2
C₂×C₄×C₁₉⋊C₈	2
C₄×C₄⋊Dic₁₉	2
#11926306	2
C₄×C₄⋊C₄×C₁₉	2
C₄×#106	19

subgroup

index

C₂×#10597265

C₂×C₄×C₁₉⋊C₈

C₄×C₄⋊Dic₁₉

#11926306

C₄×C₄⋊C₄×C₁₉

C₄×#106

Subgroups — C₄×#10597265 #14563525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#10597265 #14563525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597265 #14563525