Group #14565220 — subgroups

Subgroups — C₄×C₁₆×D₁₉ #14565220

Order 2432.

216 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 137 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×C₁₆×D₁₉	C₂	1	2	yes	maximal
2	C₄×C₈×D₁₉	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×Dic₁₉	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₁₉	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
8	C₄²×D₁₉	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
10	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₈×Dic₁₉	C₄	1	1	yes	characteristic
12	C₈×Dic₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉⋊C₁₆	C₂²	1	2	yes	—
14	C₄×C₁₉⋊C₈	C₄	1	1	yes	characteristic
15	C₁₆×D₁₉	C₄	1	8	yes	direct product factor
16	C₂×C₄×D₁₉	C₈	1	2	yes	—
17	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
20	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₄×Dic₁₉	C₈	1	2	yes	—
22	C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₈×D₁₉	C₈	1	4	yes	—
26	C₈×D₁₉	C₂×C₄	1	4	yes	—
27	C₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
28	C₁₉⋊C₁₆	C₂×C₄	1	4	yes	complemented
29	C₂²×D₁₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂×Dic₁₉	C₂×C₈	1	2	yes	—
34	C₄×D₁₉	C₁₆	1	8	yes	direct product factor
35	C₄×D₁₉	C₄²	1	2	yes	—
36	C₄×D₁₉	C₂×C₈	1	2	yes	—
37	C₈×C₁₉	C₂×C₈	1	2	yes	—
38	C₈×C₁₉	C₂²×C₄	1	2	yes	—
39	C₁₉⋊C₈	C₄²	1	2	yes	—
40	C₁₉⋊C₈	C₂×C₈	1	2	yes	—
41	C₂×C₄×C₁₆	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
43	C₂×D₁₉	C₄×C₈	1	2	yes	—
44	C₂×D₁₉	C₂×C₁₆	1	4	yes	—
45	C₄×C₁₉	C₂×C₁₆	1	4	yes	complemented
46	C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
47	C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
48	Dic₁₉	C₄×C₈	1	2	yes	—
49	Dic₁₉	C₂×C₁₆	1	4	yes	complemented
50	C₂²×C₁₆	—	19	2	no	—
51	C₂×C₄×C₈	—	19	1	no	—
52	C₄×C₁₆	—	19	2	no	—
53	C₄×C₁₆	—	19	1	no	—
54	C₄×C₁₆	D₁₉	1	1	yes	characteristic, direct product factor
55	C₂×C₁₉	C₂×C₄×C₈	1	1	yes	characteristic
56	C₂×C₁₉	C₂²×C₁₆	1	2	yes	—
57	D₁₉	C₄×C₁₆	1	4	yes	direct product factor
58	C₂²×C₈	—	19	1	no	—
59	C₂²×C₈	—	19	1	no	—
60	C₂×C₄²	—	19	1	no	—
61	C₂×C₁₆	—	19	2	no	—
62	C₂×C₁₆	—	19	8	no	—
63	C₂×C₁₆	C₂×D₁₉	1	2	yes	—
64	C₄×C₈	—	19	1	no	—
65	C₄×C₈	—	19	1	no	—
66	C₄×C₈	—	19	1	no	—
67	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
68	C₁₉	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₄	—	19	2	no	—
70	C₂²×C₄	—	19	1	no	—
71	C₂×C₈	—	19	1	no	—
72	C₂×C₈	—	19	1	no	—
73	C₂×C₈	—	19	4	no	—
74	C₂×C₈	—	19	4	no	—
75	C₂×C₈	C₄×D₁₉	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
77	C₄²	—	19	2	no	—
78	C₄²	—	19	1	no	—
79	C₄²	C₄×D₁₉	1	1	yes	characteristic
80	C₁₆	—	19	4	no	—
81	C₁₆	C₄×D₁₉	1	4	yes	direct product factor
82	C₂³	—	19	1	no	—
83	C₂×C₄	—	19	2	no	—
84	C₂×C₄	—	19	1	no	—
85	C₂×C₄	—	19	8	no	—
86	C₂×C₄	—	19	2	no	—
87	C₂×C₄	—	19	2	no	—
88	C₂×C₄	C₈×D₁₉	1	2	yes	—
89	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
90	C₈	—	19	2	no	—
91	C₈	—	19	2	no	—
92	C₈	C₈×D₁₉	1	2	yes	—
93	C₈	C₂×C₄×D₁₉	1	2	yes	—
94	C₂²	—	19	4	no	—
95	C₂²	—	19	2	no	—
96	C₂²	C₂×C₈×D₁₉	1	1	yes	characteristic
97	C₄	—	19	4	no	—
98	C₄	—	19	2	no	—
99	C₄	C₁₆×D₁₉	1	4	yes	direct product factor
100	C₄	C₄²×D₁₉	1	1	yes	characteristic
101	C₄	C₂×C₈×D₁₉	1	1	yes	characteristic
102	C₂	—	19	4	no	—
103	C₂	C₄×C₈×D₁₉	1	1	yes	characteristic
104	C₂	C₂×C₁₆×D₁₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₁₉

C₂

yes

maximal

C₄×C₈×D₁₉

C₂

yes

maximal, characteristic

C₄×C₁₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₆×Dic₁₉

C₂

yes

maximal, complemented

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₁₉

C₄

yes

characteristic

C₂×C₈×D₁₉

C₂²

yes

characteristic

C₄²×D₁₉

C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₈×Dic₁₉

C₄

yes

characteristic

C₈×Dic₁₉

C₂²

yes

characteristic

C₂×C₁₉⋊C₁₆

C₂²

yes

—

C₄×C₁₉⋊C₈

C₄

yes

characteristic

C₁₆×D₁₉

C₄

yes

direct product factor

C₂×C₄×D₁₉

C₈

yes

—

C₂×C₄×D₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×Dic₁₉

C₈

yes

—

C₄×Dic₁₉

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₈×D₁₉

C₈

yes

—

C₈×D₁₉

C₂×C₄

yes

—

C₁₆×C₁₉

C₂×C₄

yes

complemented

C₁₉⋊C₁₆

C₂×C₄

yes

complemented

C₂²×D₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

characteristic

C₂×Dic₁₉

C₂×C₈

yes

—

C₄×D₁₉

C₁₆

yes

direct product factor

C₄×D₁₉

C₄²

yes

—

C₄×D₁₉

C₂×C₈

yes

—

C₈×C₁₉

C₂×C₈

yes

—

C₈×C₁₉

C₂²×C₄

yes

—

C₁₉⋊C₈

C₄²

yes

—

C₁₉⋊C₈

C₂×C₈

yes

—

C₂×C₄×C₁₆

—

maximal, Sylow

C₂²×C₁₉

C₂²×C₈

yes

characteristic

C₂×D₁₉

C₄×C₈

yes

—

C₂×D₁₉

C₂×C₁₆

yes

—

C₄×C₁₉

C₂×C₁₆

yes

complemented

C₄×C₁₉

C₂×C₄²

yes

characteristic

C₄×C₁₉

C₂²×C₈

yes

characteristic

Dic₁₉

C₄×C₈

yes

—

Dic₁₉

C₂×C₁₆

yes

complemented

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄×C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

D₁₉

yes

characteristic, direct product factor

C₂×C₁₉

C₂×C₄×C₈

yes

characteristic

C₂×C₁₉

C₂²×C₁₆

yes

—

D₁₉

C₄×C₁₆

yes

direct product factor

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

C₂×C₄×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₉

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄²

—

C₄²

—

C₄²

C₄×D₁₉

yes

characteristic

C₁₆

—

C₁₆

C₄×D₁₉

yes

direct product factor

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₉

yes

—

C₂×C₄

C₂×C₄×D₁₉

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₁₉

yes

—

C₈

C₂×C₄×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₁₉

yes

characteristic

C₄

—

C₄

—

C₄

C₁₆×D₁₉

yes

direct product factor

100

C₄

C₄²×D₁₉

yes

characteristic

101

C₄

C₂×C₈×D₁₉

yes

characteristic

102

C₂

—

103

C₂

C₄×C₈×D₁₉

yes

characteristic

104

C₂

C₂×C₁₆×D₁₉

yes

—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	D₁₉
commutator, hypocenter	C₁₉	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₄×C₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂²×D₁₉	C₂×C₈
cosocle	C₂×C₈×C₁₉	C₂³
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄×C₁₆

subgroup

G/H

center, hypercenter

C₄×C₁₆

D₁₉

commutator, hypocenter

C₁₉

C₂×C₄×C₁₆

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₄×C₁₆×C₁₉

C₂

socle

C₂²×C₁₉

C₂²×C₈

prime radical

C₂²×D₁₉

C₂×C₈

cosocle

C₂×C₈×C₁₉

C₂³

LCS

G ▷ C₁₉

UCS

C₁ ◁ C₄×C₁₆

N	H ≅ G/N	type
3. C₄×C₁₉⋊C₁₆	C₂	semidirect
4. C₁₆×Dic₁₉	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
15. C₁₆×D₁₉	C₄	direct (N × H)
27. C₁₆×C₁₉	C₂×C₄	semidirect
28. C₁₉⋊C₁₆	C₂×C₄	semidirect
34. C₄×D₁₉	C₁₆	direct (N × H)
45. C₄×C₁₉	C₂×C₁₆	semidirect
49. Dic₁₉	C₂×C₁₆	semidirect
54. C₄×C₁₆	D₁₉	direct (N × H)
57. D₁₉	C₄×C₁₆	direct (N × H)
68. C₁₉	C₂×C₄×C₁₆	semidirect
81. C₁₆	C₄×D₁₉	direct (N × H)
99. C₄	C₁₆×D₁₉	direct (N × H)

H ≅ G/N

type

3. C₄×C₁₉⋊C₁₆

C₂

semidirect

4. C₁₆×Dic₁₉

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

15. C₁₆×D₁₉

C₄

direct (N × H)

27. C₁₆×C₁₉

C₂×C₄

semidirect

28. C₁₉⋊C₁₆

C₂×C₄

semidirect

34. C₄×D₁₉

C₁₆

direct (N × H)

45. C₄×C₁₉

C₂×C₁₆

semidirect

49. Dic₁₉

C₂×C₁₆

semidirect

54. C₄×C₁₆

D₁₉

direct (N × H)

57. D₁₉

C₄×C₁₆

direct (N × H)

68. C₁₉

C₂×C₄×C₁₆

semidirect

81. C₁₆

C₄×D₁₉

direct (N × H)

99. C₄

C₁₆×D₁₉

direct (N × H)

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

subgroup	index
C₂×C₁₆×D₁₉	2
C₄×C₈×D₁₉	2
C₄×C₁₉⋊C₁₆	2
C₁₆×Dic₁₉	2
C₄×C₁₆×C₁₉	2
C₂×C₄×C₁₆	19

subgroup

index

C₂×C₁₆×D₁₉

C₄×C₈×D₁₉

C₄×C₁₉⋊C₁₆

C₁₆×Dic₁₉

C₄×C₁₆×C₁₉

C₂×C₄×C₁₆

Subgroups — C₄×C₁₆×D₁₉ #14565220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×C16×D19 #14565220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₆×D₁₉ #14565220