Group #14559823 — subgroups

Subgroups — C₁₉×#1966 #14559823

Order 2432.

292 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 120 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×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#101	C₂	1	4	yes	maximal
4	C₄×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
8	C₁₉×C₄⋊Q₈	—	2	1	no	—
9	C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₁₉×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₄⋊C₄×C₁₉	C₄	1	4	yes	—
12	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	—	2	2	no	—
14	C₁₉×#101	—	2	8	no	—
15	C₁₉×#97	—	2	1	no	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	4	no	—
20	C₂×Q₈×C₁₉	—	2	4	no	—
21	C₂²×C₄×C₁₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	M₁₆×C₁₉	—	2	2	no	—
25	M₁₆×C₁₉	—	2	4	no	—
26	M₁₆×C₁₉	D₄	1	4	yes	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	2	4	no	—
30	C₄⋊C₄×C₁₉	—	2	4	no	—
31	C₄²×C₁₉	D₄	1	1	yes	characteristic
32	C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₄²×C₁₉	D₄	1	2	yes	—
34	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	Q₈×C₁₉	—	4	4	no	—
36	Q₈×C₁₉	—	4	2	no	—
37	Q₈×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	2	4	no	—
40	C₂×C₄×C₁₉	—	2	8	no	—
41	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	2	yes	—
47	C₈×C₁₉	—	2	4	no	—
48	C₈×C₁₉	—	4	2	no	—
49	#1966	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₁₉	—	2	2	no	—
51	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₁₉	C₄×D₄	1	2	yes	—
53	C₄×C₁₉	—	2	2	no	—
54	C₄×C₁₉	—	4	4	no	—
55	C₄×C₁₉	#101	1	4	yes	complemented
56	C₄×C₁₉	#121	1	2	yes	—
57	C₄×C₁₉	#124	1	1	yes	characteristic
58	C₄×C₁₉	#127	1	1	yes	characteristic
59	C₂×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
60	#423	C₂×C₁₉	1	1	yes	characteristic
61	C₂×#101	C₂×C₁₉	1	4	yes	—
62	C₄×M₁₆	C₂×C₁₉	1	1	yes	characteristic
63	C₂×C₁₉	—	2	2	no	—
64	C₂×C₁₉	#390	1	1	yes	characteristic
65	C₂×C₁₉	C₂×#101	1	2	yes	—
66	C₂²×Q₈	C₂²×C₁₉	1	2	yes	—
67	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
68	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
69	C₄⋊Q₈	—	2	1	no	—
70	C₄⋊Q₈	—	2	1	no	—
71	C₄⋊Q₈	—	2	2	no	—
72	C₂×C₄⋊C₄	C₄×C₁₉	1	4	yes	—
73	C₂×C₄²	C₂²×C₁₉	1	1	yes	characteristic
74	C₄⋊C₈	—	2	2	no	—
75	#101	—	2	8	no	—
76	#97	—	2	1	no	—
77	C₄×C₈	—	2	1	no	—
78	C₁₉	#1966	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×Q₈	—	2	4	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	2	no	—
82	C₂×Q₈	—	2	4	no	—
83	C₂²×C₄	C₂×C₄×C₁₉	1	4	yes	—
84	C₂²×C₄	C₂×C₄×C₁₉	1	2	yes	—
85	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	4	no	—
88	M₁₆	D₄×C₁₉	1	4	yes	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	—	2	2	no	—
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	2	4	no	—
93	C₄²	D₄×C₁₉	1	1	yes	characteristic
94	C₄²	D₄×C₁₉	1	1	yes	characteristic
95	C₄²	D₄×C₁₉	1	2	yes	—
96	C₂³	C₂²×C₄×C₁₉	1	1	yes	characteristic
97	Q₈	—	4	4	no	—
98	Q₈	—	4	2	no	—
99	Q₈	—	4	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
104	C₂×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
105	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
106	C₂×C₄	C₂×D₄×C₁₉	1	2	yes	—
107	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
108	C₂×C₄	#41×C₁₉	1	2	yes	—
109	C₈	—	2	4	no	—
110	C₈	—	4	2	no	—
111	C₂²	—	2	2	no	—
112	C₂²	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
113	C₂²	C₄×D₄×C₁₉	1	2	yes	—
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	C₁₉×#101	1	4	yes	complemented
117	C₄	C₁₉×#121	1	2	yes	—
118	C₄	C₁₉×#124	1	1	yes	characteristic
119	C₄	C₁₉×#127	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₁₉×#390	1	1	yes	characteristic
122	C₂	C₂×C₁₉×#101	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₁₉×#423

C₂

yes

maximal, characteristic

C₂×C₁₉×#101

C₂

yes

maximal

C₄×M₁₆×C₁₉

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₄

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×#101

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

D₄

yes

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1966

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

C₄×D₄

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#101

yes

complemented

C₄×C₁₉

#121

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₄⋊Q₈

C₂×C₁₉

yes

characteristic

#423

C₂×C₁₉

yes

characteristic

C₂×#101

C₂×C₁₉

yes

—

C₄×M₁₆

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#390

yes

characteristic

C₂×C₁₉

C₂×#101

yes

—

C₂²×Q₈

C₂²×C₁₉

yes

—

C₂×M₁₆

C₂²×C₁₉

yes

—

C₂×M₁₆

C₂²×C₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

C₄×C₁₉

yes

—

C₂×C₄²

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

—

#101

—

#97

—

C₄×C₈

—

C₁₉

#1966

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₂×C₄×C₁₉

yes

—

C₂²×C₄

C₂×C₄×C₁₉

yes

—

C₂²×C₄

C₂³×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

D₄×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×C₁₉

yes

characteristic

C₄²

D₄×C₁₉

yes

characteristic

C₄²

D₄×C₁₉

yes

—

C₂³

C₂²×C₄×C₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₂²⋊C₄×C₁₉

yes

—

104

C₂×C₄

C₂²⋊C₄×C₁₉

yes

—

105

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

106

C₂×C₄

C₂×D₄×C₁₉

yes

—

107

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

108

C₂×C₄

#41×C₁₉

yes

—

109

C₈

—

110

C₈

—

111

C₂²

—

112

C₂²

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

113

C₂²

C₄×D₄×C₁₉

yes

—

114

C₄

—

115

C₄

—

116

C₄

C₁₉×#101

yes

complemented

117

C₄

C₁₉×#121

yes

—

118

C₄

C₁₉×#124

yes

characteristic

119

C₄

C₁₉×#127

yes

characteristic

120

C₂

—

121

C₂

C₁₉×#390

yes

characteristic

122

C₂

C₂×C₁₉×#101

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₄×C₁₉

Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

prime radical

C₂³×C₁₉

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
49. #1966	C₁₉	direct (N × H)
55. C₄×C₁₉	#101	semidirect
78. C₁₉	#1966	direct (N × H)
116. C₄	C₁₉×#101	semidirect

H ≅ G/N

type

49. #1966

C₁₉

direct (N × H)

55. C₄×C₁₉

#101

semidirect

78. C₁₉

#1966

direct (N × H)

116. C₄

C₁₉×#101

semidirect

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

subgroup	index
C₂×C₁₉×C₄⋊Q₈	2
C₁₉×#423	2
C₂×C₁₉×#101	2
C₄×M₁₆×C₁₉	2
#1966	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

C₁₉×#423

C₂×C₁₉×#101

C₄×M₁₆×C₁₉

#1966

Subgroups — C₁₉×#1966 #14559823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1966 #14559823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1966 #14559823