Group #18013199 — subgroups

Subgroups — C₁₉×#7240 #18013199

Order 4864.

148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2166	C₂	1	2	yes	maximal
2	C₁₉×#2151	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×M₃₂	C₄	1	1	yes	characteristic
4	C₂²×C₁₆×C₁₉	C₄	1	1	yes	characteristic
5	C₁₉×#405	C₂²	1	1	yes	characteristic
6	C₁₉×#364	—	2	2	no	—
7	C₁₉×C₄⋊C₁₆	—	2	2	no	—
8	C₁₉×#349	—	2	2	no	—
9	C₁₉×#347	C₄	1	4	yes	—
10	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₁₉×#117	Q₈	1	1	yes	characteristic
13	C₁₉×M₃₂	—	2	4	no	—
14	C₁₉×M₃₂	—	4	1	no	—
15	C₂×C₁₆×C₁₉	—	2	1	no	—
16	C₂×C₁₆×C₁₉	—	2	1	no	—
17	C₂×C₁₆×C₁₉	—	4	1	no	—
18	C₁₉×#97	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₉	D₄	1	2	yes	—
20	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
21	M₁₆×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	—	2	1	no	—
23	C₂×C₈×C₁₉	—	2	1	no	—
24	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
25	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
26	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₄⋊C₄×C₁₉	—	2	1	no	—
28	C₂²⋊C₄×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	C₄⋊C₄	1	2	yes	—
30	C₁₆×C₁₉	—	4	4	no	—
31	C₁₆×C₁₉	—	4	1	no	—
32	C₁₆×C₁₉	—	4	1	no	—
33	#7240	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₁₉	#108	1	1	yes	characteristic
35	C₂×C₄×C₁₉	—	2	1	no	—
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	2	no	—
38	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
39	C₂×C₄×C₁₉	#108	1	1	yes	characteristic
40	C₈×C₁₉	—	2	2	no	—
41	C₈×C₁₉	—	2	1	no	—
42	C₈×C₁₉	#100	1	1	yes	characteristic
43	C₈×C₁₉	#101	1	1	yes	characteristic
44	#2166	C₂×C₁₉	1	2	yes	—
45	#2151	C₂×C₁₉	1	1	yes	characteristic
46	C₂²×C₁₉	—	2	1	no	—
47	C₂²×C₁₉	—	4	1	no	—
48	C₂²×C₁₉	#341	1	1	yes	characteristic
49	C₄×C₁₉	—	2	1	no	—
50	C₄×C₁₉	—	4	2	no	—
51	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
52	C₄×C₁₉	#343	1	1	yes	characteristic
53	C₂×M₃₂	C₄×C₁₉	1	1	yes	characteristic
54	C₂²×C₁₆	C₄×C₁₉	1	1	yes	characteristic
55	#405	C₂²×C₁₉	1	1	yes	characteristic
56	#364	—	2	2	no	—
57	C₄⋊C₁₆	—	2	2	no	—
58	#349	—	2	2	no	—
59	#347	C₄×C₁₉	1	4	yes	—
60	C₂×C₁₉	—	2	1	no	—
61	C₂×C₁₉	—	4	1	no	—
62	C₂×C₁₉	#1290	1	1	yes	characteristic
63	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
64	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
65	#117	Q₈×C₁₉	1	1	yes	characteristic
66	M₃₂	—	2	4	no	—
67	M₃₂	—	4	1	no	—
68	C₂×C₁₆	—	2	1	no	—
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	4	1	no	—
71	#97	C₂×C₄×C₁₉	1	2	yes	—
72	C₄×C₈	D₄×C₁₉	1	2	yes	—
73	C₁₉	#7240	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
80	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₄²	C₄⋊C₄×C₁₉	1	2	yes	—
84	C₁₆	—	4	4	no	—
85	C₁₆	—	4	1	no	—
86	C₁₆	—	4	1	no	—
87	C₂³	C₁₉×#108	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
92	C₂×C₄	C₁₉×#108	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	2	2	no	—
95	C₈	C₁₉×#100	1	1	yes	characteristic
96	C₈	C₁₉×#101	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	C₁₉×#341	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	C₁₉×H(3,ℤ/4)	1	1	yes	characteristic
103	C₄	C₁₉×#343	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	C₁₉×#1290	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2166

C₂

yes

maximal

C₁₉×#2151

C₂

yes

maximal, characteristic

C₂×C₁₉×M₃₂

C₄

yes

characteristic

C₂²×C₁₆×C₁₉

C₄

yes

characteristic

C₁₉×#405

C₂²

yes

characteristic

C₁₉×#364

—

C₁₉×C₄⋊C₁₆

—

C₁₉×#349

—

C₁₉×#347

C₄

yes

—

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

Q₈

yes

characteristic

C₁₉×M₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₁₉×#97

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₄⋊C₄

yes

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

#7240

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#108

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

—

#2151

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#341

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×M₃₂

C₄×C₁₉

yes

characteristic

C₂²×C₁₆

C₄×C₁₉

yes

characteristic

#405

C₂²×C₁₉

yes

characteristic

#364

—

C₄⋊C₁₆

—

#349

—

#347

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1290

yes

characteristic

C₂×M₁₆

D₄×C₁₉

yes

characteristic

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

#117

Q₈×C₁₉

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

C₂×C₄×C₁₉

yes

—

C₄×C₈

D₄×C₁₉

yes

—

C₁₉

#7240

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄⋊C₄×C₁₉

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

C₁₉×#108

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×#95

yes

characteristic

C₂×C₄

C₁₉×#108

yes

characteristic

C₈

—

C₈

—

C₈

C₁₉×#100

yes

characteristic

C₈

C₁₉×#101

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₁₉×#341

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

C₁₉×H(3,ℤ/4)

yes

characteristic

103

C₄

C₁₉×#343

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

C₁₉×#1290

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	H(3,ℤ/4)
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	#405	C₂²×C₁₉
socle	C₂×C₁₉	#1290
prime radical	C₂³×C₁₉	#108
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₄×C₁₉

H(3,ℤ/4)

commutator

C₂×C₈

C₄²×C₁₉

C₂²×C₁₉

C₂×C₁₉

C₂³×C₁₉

G ▷ C₂×C₈ ▷ C₄ ▷ C₁

C₁ ◁ C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
33. #7240	C₁₉	direct (N × H)
73. C₁₉	#7240	direct (N × H)

H ≅ G/N

type

33. #7240

C₁₉

direct (N × H)

73. C₁₉

#7240

direct (N × H)

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

subgroup	index
C₁₉×#2166	2
C₁₉×#2151	2
#7240	19

subgroup

index

C₁₉×#2166

C₁₉×#2151

#7240

Subgroups — C₁₉×#7240 #18013199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7240 #18013199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7240 #18013199