Group #14269703 — subgroups

Subgroups — C₁₉×#951 #14269703

Order 1824.

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

normal subgroups only

This group has 120 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	C₃×#41×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#216	C₂	1	2	yes	maximal, complemented
4	C₁₉×#214	C₂	1	2	yes	maximal, complemented
5	C₁₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#137	—	3	1	no	maximal, Hall
7	C₃×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₃×D₄×C₁₉	—	2	1	no	—
9	C₃×D₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄×C₁₉	—	2	1	no	—
11	C₂×C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₃×C₁₉	—	2	1	no	—
13	C₁₉×Dic₆	—	2	1	no	—
14	C₁₉×Dic₆	C₂²	1	2	yes	—
15	C₁₉×C₃⋊C₈	C₂²	1	2	yes	—
16	#41×C₁₉	D₃	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	3	1	no	—
18	Q₁₆×C₁₉	—	3	2	no	—
19	SD₁₆×C₁₉	—	3	2	no	—
20	M₁₆×C₁₉	—	3	1	no	—
21	C₂²×C₃×C₁₉	—	2	1	no	—
22	C₂²×C₃×C₁₉	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₉	—	2	1	no	—
24	C₃×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₃×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	Dic₃×C₁₉	—	2	2	no	—
27	Q₈×C₁₉	—	3	2	no	—
28	Q₈×C₁₉	—	6	1	no	—
29	Q₈×C₁₉	C₂×D₃	1	1	yes	characteristic
30	D₄×C₁₉	—	2	1	no	—
31	D₄×C₁₉	C₂×D₃	1	1	yes	characteristic
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	6	1	no	—
34	C₂×C₄×C₁₉	C₂×D₃	1	1	yes	characteristic
35	C₈×C₁₉	—	3	2	no	—
36	C₂×C₃×C₁₉	—	2	1	no	—
37	C₂×C₃×C₁₉	—	4	1	no	—
38	C₂×C₃×C₁₉	C₂×D₄	1	1	yes	characteristic
39	#951	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂²×C₁₉	—	2	1	no	—
41	C₂²×C₁₉	#67	1	1	yes	characteristic
42	C₄×C₁₉	—	2	1	no	—
43	C₄×C₁₉	—	6	2	no	—
44	C₄×C₁₉	#67	1	1	yes	characteristic
45	C₄×C₁₉	C₂²×D₃	1	1	yes	characteristic
46	C₃×C₁₉	#137	1	1	yes	characteristic, complemented, Hall
47	C₃×#41	C₂×C₁₉	1	1	yes	characteristic
48	C₂×Dic₆	C₂×C₁₉	1	1	yes	characteristic, complemented
49	#216	C₂×C₁₉	1	2	yes	complemented
50	#214	C₂×C₁₉	1	2	yes	complemented
51	#208	C₂×C₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	4	1	no	—
54	C₂×C₁₉	C₂×#67	1	1	yes	characteristic
55	#137	—	3	1	no	Sylow
56	C₃×Q₈	C₂²×C₁₉	1	1	yes	characteristic
57	C₃×D₄	—	2	1	no	—
58	C₃×D₄	C₂²×C₁₉	1	1	yes	characteristic
59	C₂×C₃×C₄	—	2	1	no	—
60	C₂×C₃×C₄	C₂²×C₁₉	1	1	yes	characteristic
61	C₂×Dic₃	—	2	1	no	—
62	Dic₆	—	2	1	no	—
63	Dic₆	C₂²×C₁₉	1	2	yes	—
64	C₃⋊C₈	C₂²×C₁₉	1	2	yes	—
65	C₁₉	#951	1	1	yes	characteristic, direct product factor, Sylow
66	#41	D₃×C₁₉	1	1	yes	characteristic
67	C₂×Q₈	—	3	1	no	—
68	Q₁₆	—	3	2	no	—
69	SD₁₆	—	3	2	no	—
70	M₁₆	—	3	1	no	—
71	C₂²×C₃	—	2	1	no	—
72	C₂²×C₃	D₄×C₁₉	1	1	yes	characteristic
73	C₃×C₄	—	2	1	no	—
74	C₃×C₄	D₄×C₁₉	1	1	yes	characteristic
75	C₃×C₄	C₂³×C₁₉	1	1	yes	characteristic
76	Dic₃	—	2	2	no	—
77	Q₈	—	3	2	no	—
78	Q₈	—	6	1	no	—
79	Q₈	C₂×D₃×C₁₉	1	1	yes	characteristic
80	D₄	—	2	1	no	—
81	D₄	C₂×D₃×C₁₉	1	1	yes	characteristic
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	6	1	no	—
84	C₂×C₄	C₂×D₃×C₁₉	1	1	yes	characteristic
85	C₈	—	3	2	no	—
86	C₂×C₃	—	2	1	no	—
87	C₂×C₃	—	4	1	no	—
88	C₂×C₃	C₂×D₄×C₁₉	1	1	yes	characteristic
89	C₂²	—	2	1	no	—
90	C₂²	C₁₉×#67	1	1	yes	characteristic
91	C₄	—	2	1	no	—
92	C₄	—	6	2	no	—
93	C₄	C₁₉×#67	1	1	yes	characteristic
94	C₄	C₂²×D₃×C₁₉	1	1	yes	characteristic
95	C₃	C₁₉×#137	1	1	yes	characteristic, complemented, Sylow
96	C₂	—	2	1	no	—
97	C₂	—	4	1	no	—
98	C₂	C₂×C₁₉×#67	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#41×C₁₉

C₂

yes

maximal, characteristic

C₂×C₁₉×Dic₆

C₂

yes

maximal, characteristic, complemented

C₁₉×#216

C₂

yes

maximal, complemented

C₁₉×#214

C₂

yes

maximal, complemented

C₁₉×#208

C₂

yes

maximal, characteristic, complemented

C₁₉×#137

—

maximal, Hall

C₃×Q₈×C₁₉

C₂²

yes

characteristic

C₃×D₄×C₁₉

—

C₃×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₃×C₄×C₁₉

—

C₂×C₃×C₄×C₁₉

C₂²

yes

characteristic

C₂×Dic₃×C₁₉

—

C₁₉×Dic₆

—

C₁₉×Dic₆

C₂²

yes

—

C₁₉×C₃⋊C₈

C₂²

yes

—

#41×C₁₉

D₃

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂²×C₃×C₁₉

—

C₂²×C₃×C₁₉

D₄

yes

characteristic

C₃×C₄×C₁₉

—

C₃×C₄×C₁₉

D₄

yes

characteristic

C₃×C₄×C₁₉

C₂³

yes

characteristic

Dic₃×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

C₂×D₃

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

C₂×D₃

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₃

yes

characteristic

C₈×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₂×D₄

yes

characteristic

#951

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₂²×C₁₉

—

C₂²×C₁₉

#67

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#67

yes

characteristic

C₄×C₁₉

C₂²×D₃

yes

characteristic

C₃×C₁₉

#137

yes

characteristic, complemented, Hall

C₃×#41

C₂×C₁₉

yes

characteristic

C₂×Dic₆

C₂×C₁₉

yes

characteristic, complemented

#216

C₂×C₁₉

yes

complemented

#214

C₂×C₁₉

yes

complemented

#208

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₂×#67

yes

characteristic

#137

—

Sylow

C₃×Q₈

C₂²×C₁₉

yes

characteristic

C₃×D₄

—

C₃×D₄

C₂²×C₁₉

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

C₂²×C₁₉

yes

characteristic

C₂×Dic₃

—

Dic₆

—

Dic₆

C₂²×C₁₉

yes

—

C₃⋊C₈

C₂²×C₁₉

yes

—

C₁₉

#951

yes

characteristic, direct product factor, Sylow

#41

D₃×C₁₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

SD₁₆

—

M₁₆

—

C₂²×C₃

—

C₂²×C₃

D₄×C₁₉

yes

characteristic

C₃×C₄

—

C₃×C₄

D₄×C₁₉

yes

characteristic

C₃×C₄

C₂³×C₁₉

yes

characteristic

Dic₃

—

Q₈

—

Q₈

—

Q₈

C₂×D₃×C₁₉

yes

characteristic

D₄

—

D₄

C₂×D₃×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₃×C₁₉

yes

characteristic

C₈

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₂×D₄×C₁₉

yes

characteristic

C₂²

—

C₂²

C₁₉×#67

yes

characteristic

C₄

—

C₄

—

C₄

C₁₉×#67

yes

characteristic

C₄

C₂²×D₃×C₁₉

yes

characteristic

C₃

C₁₉×#137

yes

characteristic, complemented, Sylow

C₂

—

C₂

—

C₂

C₂×C₁₉×#67

yes

characteristic

	subgroup	G/H
center	C₂×C₁₉	C₂×#67
commutator, cosocle	C₃×C₄	C₂³×C₁₉
Frattini	C₄	C₂²×D₃×C₁₉
Fitting, prime radical	C₃×#41×C₁₉	C₂
socle	C₂×C₃×C₁₉	C₂×D₄
hypercenter	#41×C₁₉	D₃
hypocenter	C₃	C₁₉×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ #41×C₁₉

subgroup

G/H

center

C₂×C₁₉

C₂×#67

commutator, cosocle

C₃×C₄

C₂³×C₁₉

Frattini

C₄

C₂²×D₃×C₁₉

Fitting, prime radical

C₃×#41×C₁₉

C₂

socle

C₂×C₃×C₁₉

C₂×D₄

hypercenter

#41×C₁₉

D₃

hypocenter

C₃

C₁₉×#137

LCS

G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ #41×C₁₉

N	H ≅ G/N	type
2. C₂×C₁₉×Dic₆	C₂	semidirect
3. C₁₉×#216	C₂	semidirect
4. C₁₉×#214	C₂	semidirect
5. C₁₉×#208	C₂	semidirect
39. #951	C₁₉	direct (N × H)
46. C₃×C₁₉	#137	semidirect
48. C₂×Dic₆	C₂×C₁₉	semidirect
49. #216	C₂×C₁₉	semidirect
50. #214	C₂×C₁₉	semidirect
51. #208	C₂×C₁₉	semidirect
65. C₁₉	#951	direct (N × H)
95. C₃	C₁₉×#137	semidirect

H ≅ G/N

type

2. C₂×C₁₉×Dic₆

C₂

semidirect

3. C₁₉×#216

C₂

semidirect

4. C₁₉×#214

C₂

semidirect

5. C₁₉×#208

C₂

semidirect

39. #951

C₁₉

direct (N × H)

46. C₃×C₁₉

#137

semidirect

48. C₂×Dic₆

C₂×C₁₉

semidirect

49. #216

C₂×C₁₉

semidirect

50. #214

C₂×C₁₉

semidirect

51. #208

C₂×C₁₉

semidirect

65. C₁₉

#951

direct (N × H)

95. C₃

C₁₉×#137

semidirect

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

subgroup	index
C₃×#41×C₁₉	2
C₂×C₁₉×Dic₆	2
C₁₉×#216	2
C₁₉×#214	2
C₁₉×#208	2
C₁₉×#137	3
#951	19

subgroup

index

C₃×#41×C₁₉

C₂×C₁₉×Dic₆

C₁₉×#216

C₁₉×#214

C₁₉×#208

C₁₉×#137

#951

Subgroups — C₁₉×#951 #14269703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#951 #14269703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#951 #14269703