Group #14560075 — subgroups

Subgroups — C₁₉×#2218 #14560075

Order 2432.

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#466	C₂	1	2	yes	maximal, complemented
4	C₁₉×#367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#357	C₂	1	2	yes	maximal, complemented
6	C₂×D₈×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#121	—	2	2	no	—
9	C₁₉×D₁₆	—	2	2	no	—
10	C₁₉×M₃₂	—	2	2	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#107	C₂²	1	2	yes	—
14	C₁₉×#102	—	2	2	no	—
15	C₂×D₄×C₁₉	—	2	2	no	—
16	C₂×D₄×C₁₉	—	4	2	no	—
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	D₈×C₁₉	—	2	2	no	—
19	D₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	—	2	1	no	—
21	C₂×C₈×C₁₉	—	2	1	no	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₂²⋊C₄×C₁₉	—	4	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	complemented
28	C₂³×C₁₉	—	4	2	no	—
29	C₂³×C₁₉	D₈	1	1	yes	characteristic
30	D₄×C₁₉	—	4	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	D₄×C₁₉	—	8	4	no	—
33	C₂×C₄×C₁₉	—	2	1	no	—
34	C₂×C₄×C₁₉	—	2	1	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
37	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₈×C₁₉	#41	1	1	yes	characteristic
41	#2218	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	2	2	no	—
44	C₂²×C₁₉	—	8	2	no	—
45	C₂²×C₁₉	—	8	2	no	—
46	C₂²×C₁₉	—	8	2	no	—
47	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	—	8	2	no	—
50	C₄×C₁₉	#121	1	1	yes	characteristic
51	C₄×C₁₉	#135	1	1	yes	characteristic
52	C₂×D₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
53	C₂×M₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#466	C₂×C₁₉	1	2	yes	complemented
55	#367	C₂×C₁₉	1	1	yes	characteristic, complemented
56	#357	C₂×C₁₉	1	2	yes	complemented
57	C₂×C₁₉	—	4	1	no	—
58	C₂×C₁₉	—	16	2	no	—
59	C₂×C₁₉	#466	1	1	yes	characteristic
60	C₂×C₁₉	#509	1	2	yes	—
61	C₂×D₈	C₂²×C₁₉	1	2	yes	—
62	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
63	#121	—	2	2	no	—
64	D₁₆	—	2	2	no	—
65	M₃₂	—	2	2	no	—
66	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
67	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
68	#107	C₂²×C₁₉	1	2	yes	—
69	#102	—	2	2	no	—
70	C₁₉	#2218	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	4	2	no	—
73	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
74	D₈	—	2	2	no	—
75	D₈	—	2	2	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
79	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
80	C₄⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	4	2	no	—
82	C₁₆	—	2	1	no	—
83	C₁₆	D₄×C₁₉	1	2	yes	complemented
84	C₂³	—	4	2	no	—
85	C₂³	D₈×C₁₉	1	1	yes	characteristic
86	D₄	—	4	2	no	—
87	D₄	—	4	2	no	—
88	D₄	—	8	4	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
96	C₈	#41×C₁₉	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	2	2	no	—
99	C₂²	—	8	2	no	—
100	C₂²	—	8	2	no	—
101	C₂²	—	8	2	no	—
102	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	8	2	no	—
105	C₄	C₁₉×#121	1	1	yes	characteristic
106	C₄	C₁₉×#135	1	1	yes	characteristic
107	C₂	—	4	1	no	—
108	C₂	—	16	2	no	—
109	C₂	C₁₉×#466	1	1	yes	characteristic
110	C₂	C₁₉×#509	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×D₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#466

C₂

yes

maximal, complemented

C₁₉×#367

C₂

yes

maximal, characteristic, complemented

C₁₉×#357

C₂

yes

maximal, complemented

C₂×D₈×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#121

—

C₁₉×D₁₆

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

—

C₁₉×#102

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

complemented

C₂³×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×D₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂×M₃₂

C₂×C₁₉

yes

characteristic, complemented

#466

C₂×C₁₉

yes

complemented

#367

C₂×C₁₉

yes

characteristic, complemented

#357

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#466

yes

characteristic

C₂×C₁₉

#509

yes

—

C₂×D₈

C₂²×C₁₉

yes

—

C₂²×C₈

C₂²×C₁₉

yes

characteristic

#121

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

—

#102

—

C₁₉

#2218

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

D₄×C₁₉

yes

complemented

C₂³

—

C₂³

D₈×C₁₉

yes

characteristic

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

C₂×D₄×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

C₂×D₈×C₁₉

yes

characteristic

103

C₄

—

104

C₄

—

105

C₄

C₁₉×#121

yes

characteristic

106

C₄

C₁₉×#135

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

C₁₉×#466

yes

characteristic

110

C₂

C₁₉×#509

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
1. C₂×C₁₉×D₁₆	C₂	semidirect
2. C₂×C₁₉×M₃₂	C₂	semidirect
3. C₁₉×#466	C₂	semidirect
4. C₁₉×#367	C₂	semidirect
5. C₁₉×#357	C₂	semidirect
27. C₁₆×C₁₉	D₄	semidirect
41. #2218	C₁₉	direct (N × H)
52. C₂×D₁₆	C₂×C₁₉	semidirect
53. C₂×M₃₂	C₂×C₁₉	semidirect
54. #466	C₂×C₁₉	semidirect
55. #367	C₂×C₁₉	semidirect
56. #357	C₂×C₁₉	semidirect
70. C₁₉	#2218	direct (N × H)
83. C₁₆	D₄×C₁₉	semidirect

H ≅ G/N

type

1. C₂×C₁₉×D₁₆

C₂

semidirect

2. C₂×C₁₉×M₃₂

C₂

semidirect

3. C₁₉×#466

C₂

semidirect

4. C₁₉×#367

C₂

semidirect

5. C₁₉×#357

C₂

semidirect

27. C₁₆×C₁₉

D₄

semidirect

41. #2218

C₁₉

direct (N × H)

52. C₂×D₁₆

C₂×C₁₉

semidirect

53. C₂×M₃₂

C₂×C₁₉

semidirect

54. #466

C₂×C₁₉

semidirect

55. #367

C₂×C₁₉

semidirect

56. #357

C₂×C₁₉

semidirect

70. C₁₉

#2218

direct (N × H)

83. C₁₆

D₄×C₁₉

semidirect

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

subgroup	index
C₂×C₁₉×D₁₆	2
C₂×C₁₉×M₃₂	2
C₁₉×#466	2
C₁₉×#367	2
C₁₉×#357	2
#2218	19

subgroup

index

C₂×C₁₉×D₁₆

C₂×C₁₉×M₃₂

C₁₉×#466

C₁₉×#367

C₁₉×#357

#2218

Subgroups — C₁₉×#2218 #14560075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2218 #14560075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2218 #14560075