Group #14560079 — subgroups

Subgroups — C₁₉×#2222 #14560079

Order 2432.

140 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 60 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×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#504	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#473	C₂	1	2	yes	maximal
4	C₁₉×#368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#362	C₂	1	2	yes	maximal, complemented
6	C₁₉×#137	—	2	2	no	—
7	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
8	C₁₉×#131	C₂²	1	1	yes	characteristic
9	C₁₉×Q₃₂	—	2	1	no	—
10	C₁₉×Q₃₂	—	2	1	no	—
11	C₁₉×M₃₂	—	2	1	no	—
12	C₁₉×M₃₂	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	—	2	1	no	—
14	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#108	C₂²	1	2	yes	—
16	C₁₉×#101	—	2	2	no	—
17	#41×C₁₉	D₄	1	1	yes	characteristic
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	Q₁₆×C₁₉	—	2	2	no	—
20	Q₁₆×C₁₉	—	2	2	no	—
21	Q₁₆×C₁₉	—	4	2	no	—
22	SD₁₆×C₁₉	—	4	2	no	—
23	M₁₆×C₁₉	—	2	1	no	—
24	M₁₆×C₁₉	—	2	2	no	—
25	M₁₆×C₁₉	D₄	1	1	yes	characteristic
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
28	C₁₆×C₁₉	—	2	1	no	—
29	C₁₆×C₁₉	D₄	1	1	yes	characteristic
30	C₁₆×C₁₉	D₄	1	1	yes	characteristic
31	Q₈×C₁₉	—	4	2	no	—
32	Q₈×C₁₉	—	4	2	no	—
33	Q₈×C₁₉	D₈	1	1	yes	characteristic
34	D₄×C₁₉	—	2	1	no	—
35	D₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	4	2	no	—
38	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	—	2	1	no	—
40	C₈×C₁₉	—	4	2	no	—
41	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₈×C₁₉	#41	1	1	yes	characteristic
43	#2222	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₁₉	—	2	1	no	—
45	C₂²×C₁₉	#135	1	1	yes	characteristic
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	2	no	—
48	C₄×C₁₉	#121	1	1	yes	characteristic
49	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
50	C₂×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
51	#504	C₂×C₁₉	1	1	yes	characteristic
52	#473	C₂×C₁₉	1	2	yes	—
53	#368	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#362	C₂×C₁₉	1	2	yes	complemented
55	C₂×C₁₉	—	2	1	no	—
56	C₂×C₁₉	—	4	1	no	—
57	C₂×C₁₉	#466	1	1	yes	characteristic
58	#137	—	2	2	no	—
59	C₂×Q₁₆	C₂²×C₁₉	1	2	yes	—
60	#131	C₂²×C₁₉	1	1	yes	characteristic
61	Q₃₂	—	2	1	no	—
62	Q₃₂	—	2	1	no	—
63	M₃₂	—	2	1	no	—
64	M₃₂	C₂²×C₁₉	1	1	yes	characteristic
65	C₂×C₁₆	—	2	1	no	—
66	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
67	#108	C₂²×C₁₉	1	2	yes	—
68	#101	—	2	2	no	—
69	C₁₉	#2222	1	1	yes	characteristic, direct product factor, Sylow
70	#41	D₄×C₁₉	1	1	yes	characteristic
71	C₂×Q₈	—	2	2	no	—
72	Q₁₆	—	2	2	no	—
73	Q₁₆	—	2	2	no	—
74	Q₁₆	—	4	2	no	—
75	SD₁₆	—	4	2	no	—
76	M₁₆	—	2	1	no	—
77	M₁₆	—	2	2	no	—
78	M₁₆	D₄×C₁₉	1	1	yes	characteristic
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
81	C₁₆	—	2	1	no	—
82	C₁₆	D₄×C₁₉	1	1	yes	characteristic
83	C₁₆	D₄×C₁₉	1	1	yes	characteristic
84	Q₈	—	4	2	no	—
85	Q₈	—	4	2	no	—
86	Q₈	D₈×C₁₉	1	1	yes	characteristic
87	D₄	—	2	1	no	—
88	D₄	D₈×C₁₉	1	1	yes	characteristic
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
92	C₈	—	2	1	no	—
93	C₈	—	4	2	no	—
94	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
95	C₈	#41×C₁₉	1	1	yes	characteristic
96	C₂²	—	2	1	no	—
97	C₂²	C₁₉×#135	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	8	2	no	—
100	C₄	C₁₉×#121	1	1	yes	characteristic
101	C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
102	C₂	—	2	1	no	—
103	C₂	—	4	1	no	—
104	C₂	C₁₉×#466	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#504

C₂

yes

maximal, characteristic

C₁₉×#473

C₂

yes

maximal

C₁₉×#368

C₂

yes

maximal, characteristic, complemented

C₁₉×#362

C₂

yes

maximal, complemented

C₁₉×#137

—

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×#131

C₂²

yes

characteristic

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₁₉×M₃₂

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#108

C₂²

yes

—

C₁₉×#101

—

#41×C₁₉

D₄

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

D₈

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

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

#135

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#121

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×Q₃₂

C₂×C₁₉

yes

characteristic, complemented

#504

C₂×C₁₉

yes

characteristic

#473

C₂×C₁₉

yes

—

#368

C₂×C₁₉

yes

characteristic, complemented

#362

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#466

yes

characteristic

#137

—

C₂×Q₁₆

C₂²×C₁₉

yes

—

#131

C₂²×C₁₉

yes

characteristic

Q₃₂

—

Q₃₂

—

M₃₂

—

M₃₂

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#108

C₂²×C₁₉

yes

—

#101

—

C₁₉

#2222

yes

characteristic, direct product factor, Sylow

#41

D₄×C₁₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

M₁₆

—

M₁₆

—

M₁₆

D₄×C₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₁₆

—

C₁₆

D₄×C₁₉

yes

characteristic

C₁₆

D₄×C₁₉

yes

characteristic

Q₈

—

Q₈

—

Q₈

D₈×C₁₉

yes

characteristic

D₄

—

D₄

D₈×C₁₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

C₂×D₄×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

C₁₉×#135

yes

characteristic

C₄

—

C₄

—

100

C₄

C₁₉×#121

yes

characteristic

101

C₄

C₂×D₈×C₁₉

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

C₁₉×#466

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	#41×C₁₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#466

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

#41×C₁₉

D₄

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×Q₃₂	C₂	semidirect
4. C₁₉×#368	C₂	semidirect
5. C₁₉×#362	C₂	semidirect
43. #2222	C₁₉	direct (N × H)
50. C₂×Q₃₂	C₂×C₁₉	semidirect
53. #368	C₂×C₁₉	semidirect
54. #362	C₂×C₁₉	semidirect
69. C₁₉	#2222	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×Q₃₂

C₂

semidirect

4. C₁₉×#368

C₂

semidirect

5. C₁₉×#362

C₂

semidirect

43. #2222

C₁₉

direct (N × H)

50. C₂×Q₃₂

C₂×C₁₉

semidirect

53. #368

C₂×C₁₉

semidirect

54. #362

C₂×C₁₉

semidirect

69. C₁₉

#2222

direct (N × H)

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

subgroup	index
C₂×C₁₉×Q₃₂	2
C₁₉×#504	2
C₁₉×#473	2
C₁₉×#368	2
C₁₉×#362	2
#2222	19

subgroup

index

C₂×C₁₉×Q₃₂

C₁₉×#504

C₁₉×#473

C₁₉×#368

C₁₉×#362

#2222

Subgroups — C₁₉×#2222 #14560079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2222 #14560079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2222 #14560079