Group #14560093 — subgroups

Subgroups — C₁₉×#2236 #14560093

Order 2432.

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

normal subgroups only

This group has 140 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	C₁₉×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#366	C₂	1	2	yes	maximal, complemented
4	C₁₉×#358	C₂	1	2	yes	maximal, complemented
5	C₁₉×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×C₂²⋊Q₈	—	2	1	no	—
9	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
10	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#107	—	2	1	no	—
12	C₁₉×#107	C₂²	1	2	yes	—
13	C₁₉×#107	C₂²	1	1	yes	characteristic
14	C₁₉×#103	—	2	1	no	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂²×C₄×C₁₉	—	4	1	no	—
17	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
18	Q₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	—	2	2	no	—
20	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₄⋊C₄×C₁₉	—	4	1	no	—
25	C₄⋊C₄×C₁₉	—	4	1	no	—
26	C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	D₈	1	1	yes	characteristic
29	Q₈×C₁₉	—	4	1	no	—
30	Q₈×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	—	4	2	no	—
36	C₂×C₄×C₁₉	—	8	2	no	—
37	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	—	2	1	no	—
40	C₈×C₁₉	#41	1	2	yes	—
41	#2236	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	2	1	no	—
44	C₂²×C₁₉	Q₃₂	1	2	yes	—
45	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	1	no	—
48	C₄×C₁₉	—	8	1	no	—
49	C₄×C₁₉	—	8	2	no	—
50	C₄×C₁₉	#123	1	1	yes	characteristic
51	C₄×C₁₉	#137	1	1	yes	characteristic
52	#467	C₂×C₁₉	1	1	yes	characteristic
53	C₂×#107	C₂×C₁₉	1	1	yes	characteristic
54	#366	C₂×C₁₉	1	2	yes	complemented
55	#358	C₂×C₁₉	1	2	yes	complemented
56	C₂²⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
57	C₂×C₁₉	—	2	2	no	—
58	C₂×C₁₉	#480	1	1	yes	characteristic
59	C₂×C₁₉	C₂×Q₃₂	1	1	yes	characteristic
60	C₂×C₁₉	#509	1	1	yes	characteristic
61	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
62	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
63	C₂²⋊Q₈	—	2	1	no	—
64	C₂×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
66	#107	—	2	1	no	—
67	#107	C₂²×C₁₉	1	2	yes	—
68	#107	C₂²×C₁₉	1	1	yes	characteristic
69	#103	—	2	1	no	—
70	C₁₉	#2236	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×Q₈	—	2	1	no	—
72	C₂²×C₄	—	4	1	no	—
73	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
74	Q₁₆	—	2	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
77	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	4	1	no	—
81	C₄⋊C₄	—	4	1	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₁₆	—	2	2	no	—
84	C₂³	D₈×C₁₉	1	1	yes	characteristic
85	Q₈	—	4	1	no	—
86	Q₈	—	4	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	4	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	—	8	2	no	—
93	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
94	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	#41×C₁₉	1	2	yes	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	C₁₉×Q₃₂	1	2	yes	—
100	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	8	1	no	—
103	C₄	—	8	2	no	—
104	C₄	—	8	1	no	—
105	C₄	C₁₉×#123	1	1	yes	characteristic
106	C₄	C₁₉×#137	1	1	yes	characteristic
107	C₂	—	2	2	no	—
108	C₂	C₁₉×#480	1	1	yes	characteristic
109	C₂	C₂×C₁₉×Q₃₂	1	1	yes	characteristic
110	C₂	C₁₉×#509	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#467

C₂

yes

maximal, characteristic

C₂×C₁₉×#107

C₂

yes

maximal, characteristic

C₁₉×#366

C₂

yes

maximal, complemented

C₁₉×#358

C₂

yes

maximal, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

—

C₁₉×#107

—

C₁₉×#107

C₂²

yes

—

C₁₉×#107

C₂²

yes

characteristic

C₁₉×#103

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₂³×C₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×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

#41

yes

—

#2236

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

Q₃₂

yes

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₂×#107

C₂×C₁₉

yes

characteristic

#366

C₂×C₁₉

yes

complemented

#358

C₂×C₁₉

yes

complemented

C₂²⋊C₁₆

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#480

yes

characteristic

C₂×C₁₉

C₂×Q₃₂

yes

characteristic

C₂×C₁₉

#509

yes

characteristic

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₁₆

C₂²×C₁₉

yes

—

#107

—

#107

C₂²×C₁₉

yes

—

#107

C₂²×C₁₉

yes

characteristic

#103

—

C₁₉

#2236

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

D₈×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

#41×C₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₁₉×Q₃₂

yes

—

100

C₂²

C₂×D₈×C₁₉

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₁₉×#123

yes

characteristic

106

C₄

C₁₉×#137

yes

characteristic

107

C₂

—

108

C₂

C₁₉×#480

yes

characteristic

109

C₂

C₂×C₁₉×Q₃₂

yes

characteristic

110

C₂

C₁₉×#509

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	D₈
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

prime radical

C₂³×C₁₉

D₈

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
3. C₁₉×#366	C₂	semidirect
4. C₁₉×#358	C₂	semidirect
41. #2236	C₁₉	direct (N × H)
54. #366	C₂×C₁₉	semidirect
55. #358	C₂×C₁₉	semidirect
70. C₁₉	#2236	direct (N × H)

H ≅ G/N

type

3. C₁₉×#366

C₂

semidirect

4. C₁₉×#358

C₂

semidirect

41. #2236

C₁₉

direct (N × H)

54. #366

C₂×C₁₉

semidirect

55. #358

C₂×C₁₉

semidirect

70. C₁₉

#2236

direct (N × H)

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

subgroup	index
C₁₉×#467	2
C₂×C₁₉×#107	2
C₁₉×#366	2
C₁₉×#358	2
C₁₉×C₂²⋊C₁₆	2
#2236	19

subgroup

index

C₁₉×#467

C₂×C₁₉×#107

C₁₉×#366

C₁₉×#358

C₁₉×C₂²⋊C₁₆

#2236

Subgroups — C₁₉×#2236 #14560093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2236 #14560093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2236 #14560093