Group #14560026 — subgroups

Subgroups — C₁₉×#2169 #14560026

Order 2432.

162 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 100 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×M₃₂	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₁₉×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×C₂²⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₁₉	C₂²	1	2	yes	—
7	C₄×D₄×C₁₉	C₄	1	1	yes	characteristic
8	C₁₉×M₃₂	—	2	4	no	—
9	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₁₉	C₂²	1	2	yes	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×C₄⋊C₈	C₄	1	1	yes	characteristic
13	C₁₉×C₂²⋊C₈	C₄	1	2	yes	—
14	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₁₉	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₉	—	2	2	no	—
18	C₂×C₈×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₉	C₈	1	1	yes	characteristic
23	C₂²⋊C₄×C₁₉	C₈	1	2	yes	—
24	C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
25	C₁₆×C₁₉	—	2	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	complemented
28	C₂³×C₁₉	C₂×C₈	1	2	yes	—
29	D₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	2	2	no	—
31	C₂×C₄×C₁₉	—	2	2	no	—
32	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₁₉	—	2	2	no	—
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2169	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	—	2	2	no	—
42	C₂²×C₁₉	—	2	2	no	—
43	C₂²×C₁₉	—	2	2	no	—
44	C₂²×C₁₉	C₂²×C₈	1	1	yes	characteristic
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	M₃₂	1	2	yes	complemented
48	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
49	C₄×C₁₉	#131	1	1	yes	characteristic
50	C₂×M₃₂	C₂×C₁₉	1	2	yes	complemented
51	C₈×D₄	C₂×C₁₉	1	1	yes	characteristic
52	C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
53	C₂²⋊C₁₆	C₂×C₁₉	1	2	yes	complemented
54	C₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
55	C₂×C₁₉	—	4	2	no	—
56	C₂×C₁₉	C₈×D₄	1	1	yes	characteristic
57	C₂×C₁₉	C₂×M₃₂	1	1	yes	characteristic
58	C₂×C₁₉	#504	1	1	yes	characteristic
59	C₂²×C₈	C₂²×C₁₉	1	2	yes	—
60	C₄×D₄	C₄×C₁₉	1	1	yes	characteristic
61	M₃₂	—	2	4	no	—
62	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
63	C₂×C₁₆	C₂²×C₁₉	1	2	yes	—
64	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
65	C₄⋊C₈	C₄×C₁₉	1	1	yes	characteristic
66	C₂²⋊C₈	C₄×C₁₉	1	2	yes	—
67	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
68	C₁₉	#2169	1	1	yes	characteristic, direct product factor, Sylow
69	C₂×D₄	C₈×C₁₉	1	1	yes	characteristic
70	C₂²×C₄	C₂×C₄×C₁₉	1	2	yes	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂×C₄×C₁₉	1	2	yes	—
75	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
76	C₄⋊C₄	C₈×C₁₉	1	1	yes	characteristic
77	C₂²⋊C₄	C₈×C₁₉	1	2	yes	—
78	C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
79	C₁₆	—	2	2	no	—
80	C₁₆	—	2	1	no	—
81	C₁₆	D₄×C₁₉	1	2	yes	complemented
82	C₂³	C₂×C₈×C₁₉	1	2	yes	—
83	D₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
87	C₂×C₄	C₂×C₈×C₁₉	1	2	yes	—
88	C₂×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
89	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	2	1	no	—
92	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
93	C₈	#41×C₁₉	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	—	2	2	no	—
96	C₂²	—	2	2	no	—
97	C₂²	C₂²×C₈×C₁₉	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	C₁₉×M₃₂	1	2	yes	complemented
101	C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
102	C₄	C₁₉×#131	1	1	yes	characteristic
103	C₂	—	4	2	no	—
104	C₂	C₈×D₄×C₁₉	1	1	yes	characteristic
105	C₂	C₂×C₁₉×M₃₂	1	1	yes	characteristic
106	C₂	C₁₉×#504	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×M₃₂

C₂

yes

maximal, complemented

C₈×D₄×C₁₉

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₁₉×C₂²⋊C₁₆

C₂

yes

maximal, complemented

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×C₁₉

C₂²

yes

—

C₄×D₄×C₁₉

C₄

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₄

yes

characteristic

C₁₉×C₂²⋊C₈

C₄

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×D₄×C₁₉

C₈

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

C₈

yes

characteristic

C₂²⋊C₄×C₁₉

C₈

yes

—

C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

complemented

C₂³×C₁₉

C₂×C₈

yes

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₈

yes

—

C₂×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₈×C₁₉

—

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×C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

M₃₂

yes

complemented

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

#131

yes

characteristic

C₂×M₃₂

C₂×C₁₉

yes

complemented

C₈×D₄

C₂×C₁₉

yes

characteristic

C₄⋊C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂²⋊C₁₆

C₂×C₁₉

yes

complemented

C₄×C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₈×D₄

yes

characteristic

C₂×C₁₉

C₂×M₃₂

yes

characteristic

C₂×C₁₉

#504

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

—

C₄×D₄

C₄×C₁₉

yes

characteristic

M₃₂

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₄×C₁₉

yes

characteristic

C₂²⋊C₈

C₄×C₁₉

yes

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2169

yes

characteristic, direct product factor, Sylow

C₂×D₄

C₈×C₁₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂×C₈

C₂×C₄×C₁₉

yes

—

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

C₈×C₁₉

yes

characteristic

C₂²⋊C₄

C₈×C₁₉

yes

—

C₄²

C₂×C₄×C₁₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

D₄×C₁₉

yes

complemented

C₂³

C₂×C₈×C₁₉

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

C₂×C₄

C₂×C₈×C₁₉

yes

—

C₂×C₄

C₂×C₈×C₁₉

yes

characteristic

C₂×C₄

C₂²×C₄×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

C₂×D₄×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂²×C₈×C₁₉

yes

characteristic

C₄

—

C₄

—

100

C₄

C₁₉×M₃₂

yes

complemented

101

C₄

C₄×D₄×C₁₉

yes

characteristic

102

C₄

C₁₉×#131

yes

characteristic

103

C₂

—

104

C₂

C₈×D₄×C₁₉

yes

characteristic

105

C₂

C₂×C₁₉×M₃₂

yes

characteristic

106

C₂

C₁₉×#504

yes

characteristic

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂×D₄×C₁₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₈×C₁₉

C₂³

commutator

C₂²

C₂²×C₈×C₁₉

Frattini, cosocle

C₂×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂²×C₈

prime radical

C₂×D₄×C₁₉

C₈

LCS

G ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×M₃₂	C₂	semidirect
3. C₁₉×C₄⋊C₁₆	C₂	semidirect
4. C₁₉×C₂²⋊C₁₆	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
27. C₁₆×C₁₉	D₄	semidirect
40. #2169	C₁₉	direct (N × H)
47. C₄×C₁₉	M₃₂	semidirect
50. C₂×M₃₂	C₂×C₁₉	semidirect
52. C₄⋊C₁₆	C₂×C₁₉	semidirect
53. C₂²⋊C₁₆	C₂×C₁₉	semidirect
54. C₄×C₁₆	C₂×C₁₉	semidirect
68. C₁₉	#2169	direct (N × H)
81. C₁₆	D₄×C₁₉	semidirect
100. C₄	C₁₉×M₃₂	semidirect

H ≅ G/N

type

1. C₂×C₁₉×M₃₂

C₂

semidirect

3. C₁₉×C₄⋊C₁₆

C₂

semidirect

4. C₁₉×C₂²⋊C₁₆

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

27. C₁₆×C₁₉

D₄

semidirect

40. #2169

C₁₉

direct (N × H)

47. C₄×C₁₉

M₃₂

semidirect

50. C₂×M₃₂

C₂×C₁₉

semidirect

52. C₄⋊C₁₆

C₂×C₁₉

semidirect

53. C₂²⋊C₁₆

C₂×C₁₉

semidirect

54. C₄×C₁₆

C₂×C₁₉

semidirect

68. C₁₉

#2169

direct (N × H)

81. C₁₆

D₄×C₁₉

semidirect

100. C₄

C₁₉×M₃₂

semidirect

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

subgroup	index
C₂×C₁₉×M₃₂	2
C₈×D₄×C₁₉	2
C₁₉×C₄⋊C₁₆	2
C₁₉×C₂²⋊C₁₆	2
C₄×C₁₆×C₁₉	2
#2169	19

subgroup

index

C₂×C₁₉×M₃₂

C₈×D₄×C₁₉

C₁₉×C₄⋊C₁₆

C₁₉×C₂²⋊C₁₆

C₄×C₁₆×C₁₉

#2169

Subgroups — C₁₉×#2169 #14560026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2169 #14560026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2169 #14560026