Group #14559533 — subgroups

Subgroups — C₁₉×#1676 #14559533

Order 2432.

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

normal subgroups only

This group has 144 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×#477	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×#333	C₂	1	2	yes	maximal
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#107	—	2	1	no	—
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	—	2	2	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	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	Q₈×C₁₉	—	2	1	no	—
30	Q₈×C₁₉	—	8	2	no	—
31	Q₈×C₁₉	Q₁₆	1	2	yes	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	—	4	2	no	—
40	C₈×C₁₉	—	4	1	no	—
41	C₈×C₁₉	Q₁₆	1	2	yes	—
42	#1676	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₁₉	#121	1	1	yes	characteristic
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	2	1	no	—
46	C₄×C₁₉	—	4	1	no	—
47	C₄×C₁₉	—	8	2	no	—
48	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
49	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
50	C₄×C₁₉	#135	1	1	yes	characteristic
51	C₄×C₁₉	#137	1	1	yes	characteristic
52	#500	C₂×C₁₉	1	1	yes	characteristic
53	#477	C₂×C₁₉	1	2	yes	—
54	C₈×Q₈	C₂×C₁₉	1	1	yes	characteristic
55	#335	C₂×C₁₉	1	1	yes	characteristic
56	#333	C₂×C₁₉	1	2	yes	—
57	C₂×C₁₉	#462	1	1	yes	characteristic
58	C₂×C₁₉	#467	1	1	yes	characteristic
59	C₂×C₁₉	#472	1	1	yes	characteristic
60	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
61	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
62	#107	—	2	1	no	—
63	#107	—	2	1	no	—
64	#107	—	2	2	no	—
65	C₄⋊C₈	—	2	1	no	—
66	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
67	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
68	#103	—	2	2	no	—
69	C₄×C₈	—	2	1	no	—
70	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
71	C₁₉	#1676	1	1	yes	characteristic, direct product factor, Sylow
72	C₂×Q₈	—	2	2	no	—
73	C₂×Q₈	D₄×C₁₉	1	1	yes	characteristic
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
82	C₄²	—	2	1	no	—
83	C₄²	C₂³×C₁₉	1	1	yes	characteristic
84	Q₈	—	2	1	no	—
85	Q₈	—	8	2	no	—
86	Q₈	Q₁₆×C₁₉	1	2	yes	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
91	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
92	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	4	2	no	—
95	C₈	—	4	1	no	—
96	C₈	Q₁₆×C₁₉	1	2	yes	—
97	C₂²	C₁₉×#121	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	8	2	no	—
102	C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
103	C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
104	C₄	C₁₉×#135	1	1	yes	characteristic
105	C₄	C₁₉×#137	1	1	yes	characteristic
106	C₂	C₁₉×#462	1	1	yes	characteristic
107	C₂	C₁₉×#467	1	1	yes	characteristic
108	C₂	C₁₉×#472	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic

C₁₉×#477

C₂

yes

maximal

C₈×Q₈×C₁₉

C₂

yes

maximal, characteristic

C₁₉×#335

C₂

yes

maximal, characteristic

C₁₉×#333

C₂

yes

maximal

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#107

—

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

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

Q₁₆

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

—

#1676

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

characteristic

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

#477

C₂×C₁₉

yes

—

C₈×Q₈

C₂×C₁₉

yes

characteristic

#335

C₂×C₁₉

yes

characteristic

#333

C₂×C₁₉

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

C₂²×C₁₉

yes

—

C₄×Q₈

C₂²×C₁₉

yes

—

—

—

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₂²×C₁₉

yes

—

#103

—

C₄×C₈

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#1676

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

D₄×C₁₉

yes

characteristic

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

Q₁₆×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

—

C₈

Q₁₆×C₁₉

yes

—

C₂²

C₁₉×#121

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

C₂×Q₁₆×C₁₉

yes

characteristic

103

C₄

C₂×Q₁₆×C₁₉

yes

characteristic

104

C₄

C₁₉×#135

yes

characteristic

105

C₄

C₁₉×#137

yes

characteristic

106

C₂

C₁₉×#462

yes

characteristic

107

C₂

C₁₉×#467

yes

characteristic

108

C₂

C₁₉×#472

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
42. #1676	C₁₉	direct (N × H)
71. C₁₉	#1676	direct (N × H)

H ≅ G/N

type

42. #1676

C₁₉

direct (N × H)

71. C₁₉

#1676

direct (N × H)

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

subgroup	index
C₁₉×#500	2
C₁₉×#477	2
C₈×Q₈×C₁₉	2
C₁₉×#335	2
C₁₉×#333	2
#1676	19

subgroup

index

C₁₉×#500

C₁₉×#477

C₈×Q₈×C₁₉

C₁₉×#335

C₁₉×#333

#1676

Subgroups — C₁₉×#1676 #14559533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1676 #14559533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1676 #14559533