Group #18013345 — subgroups

Subgroups — C₁₉×#7386 #18013345

Order 4864.

124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₄×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic
5	C₄×Q₁₆×C₁₉	—	2	1	no	—
6	C₂×C₁₉×C₃₂	—	2	1	no	—
7	C₁₉×#366	C₄	1	1	yes	characteristic
8	C₁₉×#358	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#335	—	2	1	no	—
11	C₂×Q₁₆×C₁₉	—	2	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₁₉×Q₃₂	—	2	1	no	—
14	C₁₉×Q₃₂	C₈	1	2	yes	complemented
15	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₁₉×#107	—	2	1	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×#103	—	4	1	no	—
20	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₁₉×C₃₂	—	2	2	no	—
22	C₂×Q₈×C₁₉	—	4	1	no	—
23	Q₁₆×C₁₉	—	2	2	no	—
24	Q₁₆×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	—	8	1	no	—
26	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
28	C₄⋊C₄×C₁₉	—	4	1	no	—
29	C₄⋊C₄×C₁₉	—	8	1	no	—
30	C₄²×C₁₉	—	8	1	no	—
31	C₄²×C₁₉	D₈	1	1	yes	characteristic
32	C₁₆×C₁₉	—	2	1	no	—
33	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
35	#7386	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	Q₈×C₁₉	—	4	2	no	—
37	Q₈×C₁₉	—	8	1	no	—
38	C₂×C₄×C₁₉	—	8	1	no	—
39	C₂×C₄×C₁₉	—	8	1	no	—
40	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
41	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
42	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	—	16	1	no	—
45	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
46	C₈×C₁₉	#104	1	1	yes	characteristic
47	C₄×Q₃₂	C₂×C₁₉	1	1	yes	characteristic
48	#1397	C₂×C₁₉	1	1	yes	characteristic
49	#1372	C₂×C₁₉	1	1	yes	characteristic
50	C₂²×C₁₉	#357	1	1	yes	characteristic
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	—	8	2	no	—
54	C₄×C₁₉	—	16	1	no	—
55	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
56	C₄×C₁₉	#359	1	1	yes	characteristic
57	C₂×Q₃₂	C₄×C₁₉	1	1	yes	characteristic
58	C₄×Q₁₆	—	2	1	no	—
59	C₂×C₃₂	—	2	1	no	—
60	#366	C₄×C₁₉	1	1	yes	characteristic
61	#358	—	2	1	no	—
62	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
63	#335	—	2	1	no	—
64	C₂×C₁₉	#1331	1	1	yes	characteristic
65	C₂×C₁₉	#1418	1	1	yes	characteristic
66	C₂×C₁₉	#1420	1	1	yes	characteristic
67	C₂×Q₁₆	—	2	1	no	—
68	C₄×Q₈	—	4	1	no	—
69	Q₃₂	—	2	1	no	—
70	Q₃₂	C₈×C₁₉	1	2	yes	complemented
71	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
72	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
73	#107	—	2	1	no	—
74	C₄⋊C₈	—	4	1	no	—
75	#103	—	4	1	no	—
76	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₃₂	—	2	2	no	—
78	C₁₉	#7386	1	1	yes	characteristic, direct product factor, Sylow
79	C₂×Q₈	—	4	1	no	—
80	Q₁₆	—	2	2	no	—
81	Q₁₆	—	4	1	no	—
82	C₂×C₈	—	8	1	no	—
83	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
84	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
85	C₄⋊C₄	—	4	1	no	—
86	C₄⋊C₄	—	8	1	no	—
87	C₄²	—	8	1	no	—
88	C₄²	D₈×C₁₉	1	1	yes	characteristic
89	C₁₆	—	2	1	no	—
90	C₁₆	C₂×C₈×C₁₉	1	1	yes	characteristic
91	C₁₆	M₁₆×C₁₉	1	1	yes	characteristic
92	Q₈	—	4	2	no	—
93	Q₈	—	8	1	no	—
94	C₂×C₄	—	8	1	no	—
95	C₂×C₄	—	8	1	no	—
96	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
97	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
98	C₂×C₄	C₁₉×SD₃₂	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	16	1	no	—
101	C₈	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
102	C₈	C₁₉×#104	1	1	yes	characteristic
103	C₂²	C₁₉×#357	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	2	no	—
107	C₄	—	16	1	no	—
108	C₄	C₁₉×D₄⋊C₈	1	1	yes	characteristic
109	C₄	C₁₉×#359	1	1	yes	characteristic
110	C₂	C₁₉×#1331	1	1	yes	characteristic
111	C₂	C₁₉×#1418	1	1	yes	characteristic
112	C₂	C₁₉×#1420	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×C₁₉×Q₃₂

C₂

yes

maximal, characteristic

C₁₉×#1397

C₂

yes

maximal, characteristic

C₁₉×#1372

C₂

yes

maximal, characteristic

C₂×C₁₉×Q₃₂

C₄

yes

characteristic

C₄×Q₁₆×C₁₉

—

C₂×C₁₉×C₃₂

—

C₁₉×#366

C₄

yes

characteristic

C₁₉×#358

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×Q₁₆×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

C₈

yes

complemented

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

characteristic

#7386

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

#104

yes

characteristic

C₄×Q₃₂

C₂×C₁₉

yes

characteristic

#1397

C₂×C₁₉

yes

characteristic

#1372

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#359

yes

characteristic

C₂×Q₃₂

C₄×C₁₉

yes

characteristic

C₄×Q₁₆

—

C₂×C₃₂

—

#366

C₄×C₁₉

yes

characteristic

#358

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

#335

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

C₈×C₁₉

yes

complemented

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#7386

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

SD₁₆×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

D₈×C₁₉

yes

characteristic

C₁₆

—

C₁₆

C₂×C₈×C₁₉

yes

characteristic

C₁₆

M₁₆×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×#102

yes

characteristic

C₂×C₄

C₁₉×D₁₆

yes

characteristic

C₂×C₄

C₁₉×SD₃₂

yes

characteristic

C₈

—

100

C₈

—

101

C₈

C₁₉×C₂²⋊C₈

yes

characteristic

102

C₈

C₁₉×#104

yes

characteristic

103

C₂²

C₁₉×#357

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

C₁₉×D₄⋊C₈

yes

characteristic

109

C₄

C₁₉×#359

yes

characteristic

110

C₂

C₁₉×#1331

yes

characteristic

111

C₂

C₁₉×#1418

yes

characteristic

112

C₂

C₁₉×#1420

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#357
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

#357

commutator

C₁₆

C₂×C₈×C₁₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₁₉

LCS

G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
14. C₁₉×Q₃₂	C₈	semidirect
35. #7386	C₁₉	direct (N × H)
70. Q₃₂	C₈×C₁₉	semidirect
78. C₁₉	#7386	direct (N × H)

H ≅ G/N

type

14. C₁₉×Q₃₂

C₈

semidirect

35. #7386

C₁₉

direct (N × H)

70. Q₃₂

C₈×C₁₉

semidirect

78. C₁₉

#7386

direct (N × H)

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

subgroup	index
C₄×C₁₉×Q₃₂	2
C₁₉×#1397	2
C₁₉×#1372	2
#7386	19

subgroup

index

C₄×C₁₉×Q₃₂

C₁₉×#1397

C₁₉×#1372

#7386

Subgroups — C₁₉×#7386 #18013345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7386 #18013345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7386 #18013345