Group #14269681 — subgroups

Subgroups — C₁₉×#929 #14269681

Order 1824.

156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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	C₂²×C₃×C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#67	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₁₉×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₁₉×#123	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×D₃×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₉	—	2	2	no	—
10	C₂×C₃×C₄×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#67	—	2	2	no	—
12	C₂×Dic₃×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₃×C₁₉	C₂²	1	2	yes	—
14	C₂×D₄×C₁₉	—	3	1	no	—
15	C₂²×C₄×C₁₉	D₃	1	1	yes	characteristic, complemented
16	C₄⋊C₄×C₁₉	—	3	2	no	—
17	C₂²⋊C₄×C₁₉	—	3	1	no	—
18	C₂²⋊C₄×C₁₉	—	3	2	no	—
19	C₂²×C₃×C₁₉	—	2	2	no	—
20	C₂²×C₃×C₁₉	D₄	1	2	yes	—
21	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×D₃×C₁₉	—	2	1	no	—
23	C₂×D₃×C₁₉	—	2	2	no	—
24	C₃×C₄×C₁₉	—	2	2	no	—
25	Dic₃×C₁₉	—	2	1	no	—
26	Dic₃×C₁₉	—	2	2	no	—
27	C₂³×C₁₉	—	3	1	no	—
28	C₂³×C₁₉	C₂×D₃	1	1	yes	characteristic
29	D₄×C₁₉	—	6	2	no	—
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	3	2	no	—
32	C₂×C₄×C₁₉	—	3	1	no	—
33	C₂×C₄×C₁₉	C₂×D₃	1	2	yes	—
34	C₂×C₃×C₁₉	—	2	2	no	—
35	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₃×C₁₉	#41	1	2	yes	—
37	D₃×C₁₉	—	4	1	no	—
38	#929	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂²×C₁₉	—	2	2	no	—
40	C₂²×C₁₉	—	6	2	no	—
41	C₂²×C₁₉	—	6	1	no	—
42	C₂²×C₁₉	#67	1	2	yes	—
43	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
44	C₄×C₁₉	—	2	2	no	—
45	C₄×C₁₉	—	6	2	no	—
46	C₄×C₁₉	—	6	1	no	—
47	C₃×C₁₉	#123	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₃×C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
49	C₂×#67	C₂×C₁₉	1	1	yes	characteristic
50	#217	C₂×C₁₉	1	1	yes	characteristic, complemented
51	(C₂×D₃)⋊C₄	C₂×C₁₉	1	2	yes	complemented
52	Dic₃⋊C₄	C₂×C₁₉	1	2	yes	complemented
53	C₂×C₁₉	—	2	2	no	—
54	C₂×C₁₉	—	12	1	no	—
55	C₂×C₁₉	#235	1	2	yes	—
56	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
57	#123	—	3	1	no	Sylow
58	C₂³×C₃	C₂²×C₁₉	1	1	yes	characteristic
59	C₂²×D₃	C₂²×C₁₉	1	1	yes	characteristic
60	C₂×C₃×C₄	—	2	2	no	—
61	C₂×C₃×C₄	C₂²×C₁₉	1	2	yes	—
62	#67	—	2	2	no	—
63	C₂×Dic₃	C₂²×C₁₉	1	1	yes	characteristic
64	C₂×Dic₃	C₂²×C₁₉	1	2	yes	—
65	C₁₉	#929	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×D₄	—	3	1	no	—
67	C₂²×C₄	D₃×C₁₉	1	1	yes	characteristic, complemented
68	C₄⋊C₄	—	3	2	no	—
69	C₂²⋊C₄	—	3	1	no	—
70	C₂²⋊C₄	—	3	2	no	—
71	C₂²×C₃	—	2	2	no	—
72	C₂²×C₃	D₄×C₁₉	1	2	yes	—
73	C₂²×C₃	C₂³×C₁₉	1	1	yes	characteristic
74	C₂×D₃	—	2	1	no	—
75	C₂×D₃	—	2	2	no	—
76	C₃×C₄	—	2	2	no	—
77	Dic₃	—	2	1	no	—
78	Dic₃	—	2	2	no	—
79	C₂³	—	3	1	no	—
80	C₂³	C₂×D₃×C₁₉	1	1	yes	characteristic
81	D₄	—	6	2	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	3	2	no	—
84	C₂×C₄	—	3	1	no	—
85	C₂×C₄	C₂×D₃×C₁₉	1	2	yes	—
86	C₂×C₃	—	2	2	no	—
87	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
88	C₂×C₃	#41×C₁₉	1	2	yes	—
89	D₃	—	4	1	no	—
90	C₂²	—	2	2	no	—
91	C₂²	—	6	2	no	—
92	C₂²	—	6	1	no	—
93	C₂²	C₁₉×#67	1	2	yes	—
94	C₂²	C₂²×D₃×C₁₉	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	6	2	no	—
97	C₄	—	6	1	no	—
98	C₃	C₁₉×#123	1	1	yes	characteristic, complemented, Sylow
99	C₂	—	2	2	no	—
100	C₂	—	12	1	no	—
101	C₂	C₁₉×#235	1	2	yes	—
102	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₃×C₄×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×#67

C₂

yes

maximal, characteristic

C₁₉×#217

C₂

yes

maximal, characteristic, complemented

C₁₉×(C₂×D₃)⋊C₄

C₂

yes

maximal, complemented

C₁₉×Dic₃⋊C₄

C₂

yes

maximal, complemented

C₁₉×#123

—

maximal, Hall

C₂³×C₃×C₁₉

C₂²

yes

characteristic

C₂²×D₃×C₁₉

C₂²

yes

characteristic

C₂×C₃×C₄×C₁₉

—

C₂×C₃×C₄×C₁₉

C₂²

yes

—

C₁₉×#67

—

C₂×Dic₃×C₁₉

C₂²

yes

characteristic

C₂×Dic₃×C₁₉

C₂²

yes

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

D₃

yes

characteristic, complemented

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²×C₃×C₁₉

—

C₂²×C₃×C₁₉

D₄

yes

—

C₂²×C₃×C₁₉

C₂³

yes

characteristic

C₂×D₃×C₁₉

—

C₂×D₃×C₁₉

—

C₃×C₄×C₁₉

—

Dic₃×C₁₉

—

Dic₃×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×D₃

yes

characteristic

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

C₂×C₃×C₁₉

#41

yes

—

D₃×C₁₉

—

#929

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#67

yes

—

C₂²×C₁₉

C₂²×D₃

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₃×C₁₉

#123

yes

characteristic, complemented, Hall

C₂²×C₃×C₄

C₂×C₁₉

yes

characteristic, complemented

C₂×#67

C₂×C₁₉

yes

characteristic

#217

C₂×C₁₉

yes

characteristic, complemented

(C₂×D₃)⋊C₄

C₂×C₁₉

yes

complemented

Dic₃⋊C₄

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#235

yes

—

C₂×C₁₉

C₂×#67

yes

characteristic

#123

—

Sylow

C₂³×C₃

C₂²×C₁₉

yes

characteristic

C₂²×D₃

C₂²×C₁₉

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₁₉

yes

—

#67

—

C₂×Dic₃

C₂²×C₁₉

yes

characteristic

C₂×Dic₃

C₂²×C₁₉

yes

—

C₁₉

#929

yes

characteristic, direct product factor, Sylow

C₂×D₄

—

C₂²×C₄

D₃×C₁₉

yes

characteristic, complemented

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²×C₃

—

C₂²×C₃

D₄×C₁₉

yes

—

C₂²×C₃

C₂³×C₁₉

yes

characteristic

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

Dic₃

—

Dic₃

—

C₂³

—

C₂³

C₂×D₃×C₁₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₃×C₁₉

yes

—

C₂×C₃

—

C₂×C₃

C₂×D₄×C₁₉

yes

characteristic

C₂×C₃

#41×C₁₉

yes

—

D₃

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₉×#67

yes

—

C₂²

C₂²×D₃×C₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₃

C₁₉×#123

yes

characteristic, complemented, Sylow

C₂

—

100

C₂

—

101

C₂

C₁₉×#235

yes

—

102

C₂

C₂×C₁₉×#67

yes

characteristic

	subgroup	G/H
center	C₂²×C₁₉	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₉
Frattini	C₂²	C₂²×D₃×C₁₉
Fitting	C₂²×C₃×C₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂×C₁₉×#67	C₂
hypercenter	C₂²×C₄×C₁₉	D₃
hypocenter	C₃	C₁₉×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉

subgroup

G/H

center

C₂²×C₁₉

C₂²×D₃

commutator, cosocle

C₂²×C₃

C₂³×C₁₉

Frattini

C₂²

C₂²×D₃×C₁₉

Fitting

C₂²×C₃×C₄×C₁₉

C₂

socle

C₂²×C₃×C₁₉

C₂³

prime radical

C₂×C₁₉×#67

C₂

hypercenter

C₂²×C₄×C₁₉

D₃

hypocenter

C₃

C₁₉×#123

LCS

G ▷ C₂²×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉

N	H ≅ G/N	type
1. C₂²×C₃×C₄×C₁₉	C₂	semidirect
3. C₁₉×#217	C₂	semidirect
4. C₁₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₁₉×Dic₃⋊C₄	C₂	semidirect
15. C₂²×C₄×C₁₉	D₃	semidirect
38. #929	C₁₉	direct (N × H)
47. C₃×C₁₉	#123	semidirect
48. C₂²×C₃×C₄	C₂×C₁₉	semidirect
50. #217	C₂×C₁₉	semidirect
51. (C₂×D₃)⋊C₄	C₂×C₁₉	semidirect
52. Dic₃⋊C₄	C₂×C₁₉	semidirect
65. C₁₉	#929	direct (N × H)
67. C₂²×C₄	D₃×C₁₉	semidirect
98. C₃	C₁₉×#123	semidirect

H ≅ G/N

type

1. C₂²×C₃×C₄×C₁₉

C₂

semidirect

3. C₁₉×#217

C₂

semidirect

4. C₁₉×(C₂×D₃)⋊C₄

C₂

semidirect

5. C₁₉×Dic₃⋊C₄

C₂

semidirect

15. C₂²×C₄×C₁₉

D₃

semidirect

38. #929

C₁₉

direct (N × H)

47. C₃×C₁₉

#123

semidirect

48. C₂²×C₃×C₄

C₂×C₁₉

semidirect

50. #217

C₂×C₁₉

semidirect

51. (C₂×D₃)⋊C₄

C₂×C₁₉

semidirect

52. Dic₃⋊C₄

C₂×C₁₉

semidirect

65. C₁₉

#929

direct (N × H)

67. C₂²×C₄

D₃×C₁₉

semidirect

98. C₃

C₁₉×#123

semidirect

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

subgroup	index
C₂²×C₃×C₄×C₁₉	2
C₂×C₁₉×#67	2
C₁₉×#217	2
C₁₉×(C₂×D₃)⋊C₄	2
C₁₉×Dic₃⋊C₄	2
C₁₉×#123	3
#929	19

subgroup

index

C₂²×C₃×C₄×C₁₉

C₂×C₁₉×#67

C₁₉×#217

C₁₉×(C₂×D₃)⋊C₄

C₁₉×Dic₃⋊C₄

C₁₉×#123

#929

Subgroups — C₁₉×#929 #14269681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#929 #14269681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#929 #14269681