Group #14559531 — subgroups

Subgroups — C₁₉×#1674 #14559531

Order 2432.

156 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 72 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	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#462	C₂	1	2	yes	maximal
3	C₈×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#335	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#332	C₂	1	2	yes	maximal
6	C₂×Q₁₆×C₁₉	—	2	2	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	—	2	1	no	—
11	C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#103	—	2	2	no	—
15	C₄×C₈×C₁₉	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
19	Q₁₆×C₁₉	—	4	4	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
28	C₄²×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	C₂³	1	1	yes	characteristic
30	Q₈×C₁₉	—	2	1	no	—
31	Q₈×C₁₉	—	4	2	no	—
32	Q₈×C₁₉	—	4	2	no	—
33	Q₈×C₁₉	D₈	1	2	yes	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	4	2	no	—
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
40	C₈×C₁₉	—	2	1	no	—
41	C₈×C₁₉	—	4	2	no	—
42	C₈×C₁₉	—	4	1	no	—
43	C₈×C₁₉	Q₁₆	1	2	yes	complemented
44	#1674	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₁₉	#121	1	1	yes	characteristic
46	C₄×C₁₉	—	2	2	no	—
47	C₄×C₁₉	—	2	1	no	—
48	C₄×C₁₉	—	4	1	no	—
49	C₄×C₁₉	—	8	2	no	—
50	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
51	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₄×C₁₉	#135	1	1	yes	characteristic
53	C₄×C₁₉	#137	1	1	yes	characteristic
54	#500	C₂×C₁₉	1	1	yes	characteristic
55	#462	C₂×C₁₉	1	2	yes	—
56	C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic
57	#335	C₂×C₁₉	1	1	yes	characteristic
58	#332	C₂×C₁₉	1	2	yes	—
59	C₂×C₁₉	#462	1	1	yes	characteristic
60	C₂×C₁₉	#466	1	1	yes	characteristic
61	C₂×C₁₉	#473	1	1	yes	characteristic
62	C₂×Q₁₆	—	2	2	no	—
63	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
64	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
65	#107	—	2	1	no	—
66	#107	—	2	1	no	—
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
69	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
70	#103	—	2	2	no	—
71	C₄×C₈	—	2	1	no	—
72	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
73	C₁₉	#1674	1	1	yes	characteristic, direct product factor, Sylow
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	D₄×C₁₉	1	1	yes	characteristic
76	Q₁₆	—	4	4	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
80	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	2	2	no	—
84	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
85	C₄²	—	2	1	no	—
86	C₄²	C₂³×C₁₉	1	1	yes	characteristic
87	Q₈	—	2	1	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	4	2	no	—
90	Q₈	D₈×C₁₉	1	2	yes	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	4	2	no	—
94	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
95	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
96	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
97	C₈	—	2	1	no	—
98	C₈	—	4	2	no	—
99	C₈	—	4	1	no	—
100	C₈	Q₁₆×C₁₉	1	2	yes	complemented
101	C₂²	C₁₉×#121	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	2	1	no	—
104	C₄	—	4	1	no	—
105	C₄	—	8	2	no	—
106	C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
107	C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
108	C₄	C₁₉×#135	1	1	yes	characteristic
109	C₄	C₁₉×#137	1	1	yes	characteristic
110	C₂	C₁₉×#462	1	1	yes	characteristic
111	C₂	C₁₉×#466	1	1	yes	characteristic
112	C₂	C₁₉×#473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic

C₁₉×#462

C₂

yes

maximal

C₈×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#335

C₂

yes

maximal, characteristic

C₁₉×#332

C₂

yes

maximal

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

D₈

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

complemented

#1674

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

#462

C₂×C₁₉

yes

—

C₈×Q₈

C₂×C₁₉

yes

characteristic

#335

C₂×C₁₉

yes

characteristic

#332

C₂×C₁₉

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄⋊Q₈

C₂²×C₁₉

yes

—

C₄×Q₈

C₂²×C₁₉

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₂²×C₁₉

yes

—

#103

—

C₄×C₈

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#1674

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

D₄×C₁₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₄²

—

C₄²

C₂³×C₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

D₈×C₁₉

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

#41×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

100

C₈

Q₁₆×C₁₉

yes

complemented

101

C₂²

C₁₉×#121

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

C₂×D₈×C₁₉

yes

characteristic

107

C₄

C₂×Q₁₆×C₁₉

yes

characteristic

108

C₄

C₁₉×#135

yes

characteristic

109

C₄

C₁₉×#137

yes

characteristic

110

C₂

C₁₉×#462

yes

characteristic

111

C₂

C₁₉×#466

yes

characteristic

112

C₂

C₁₉×#473

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

#121

commutator, Frattini, cosocle

C₄²

C₂³×C₁₉

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
43. C₈×C₁₉	Q₁₆	semidirect
44. #1674	C₁₉	direct (N × H)
73. C₁₉	#1674	direct (N × H)
100. C₈	Q₁₆×C₁₉	semidirect

H ≅ G/N

type

43. C₈×C₁₉

Q₁₆

semidirect

44. #1674

C₁₉

direct (N × H)

73. C₁₉

#1674

direct (N × H)

100. C₈

Q₁₆×C₁₉

semidirect

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

subgroup	index
C₁₉×#500	2
C₁₉×#462	2
C₈×Q₈×C₁₉	2
C₁₉×#335	2
C₁₉×#332	2
#1674	19

subgroup

index

C₁₉×#500

C₁₉×#462

C₈×Q₈×C₁₉

C₁₉×#335

C₁₉×#332

#1674

Subgroups — C₁₉×#1674 #14559531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1674 #14559531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1674 #14559531