Group #14560076 — subgroups

Subgroups — C₁₉×#2219 #14560076

Order 2432.

150 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 64 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	C₂×C₁₉×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#467	C₂	1	2	yes	maximal
4	C₁₉×#367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#358	C₂	1	2	yes	maximal, complemented
6	C₂×Q₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×C₂²⋊Q₈	—	2	2	no	—
9	C₁₉×Q₃₂	—	2	2	no	—
10	C₁₉×M₃₂	—	2	2	no	—
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#107	C₂²	1	2	yes	—
14	C₁₉×#103	—	2	2	no	—
15	C₂×Q₈×C₁₉	—	2	2	no	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₉	—	2	2	no	—
18	Q₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	—	2	1	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄⋊C₄×C₁₉	—	4	2	no	—
25	C₂²⋊C₄×C₁₉	—	4	2	no	—
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	D₄	1	2	yes	—
28	C₂³×C₁₉	D₈	1	1	yes	characteristic
29	Q₈×C₁₉	—	4	2	no	—
30	Q₈×C₁₉	—	4	2	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	2	no	—
34	C₂×C₄×C₁₉	—	4	2	no	—
35	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2219	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	2	2	no	—
43	C₂²×C₁₉	C₂×D₈	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	8	2	no	—
46	C₄×C₁₉	—	8	2	no	—
47	C₄×C₁₉	#121	1	1	yes	characteristic
48	C₄×C₁₉	#135	1	1	yes	characteristic
49	C₂×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
50	C₂×M₃₂	C₂×C₁₉	1	1	yes	characteristic
51	#467	C₂×C₁₉	1	2	yes	—
52	#367	C₂×C₁₉	1	1	yes	characteristic, complemented
53	#358	C₂×C₁₉	1	2	yes	complemented
54	C₂×C₁₉	—	4	1	no	—
55	C₂×C₁₉	#466	1	1	yes	characteristic
56	C₂×C₁₉	#510	1	2	yes	—
57	C₂×Q₁₆	C₂²×C₁₉	1	2	yes	—
58	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
59	C₂²⋊Q₈	—	2	2	no	—
60	Q₃₂	—	2	2	no	—
61	M₃₂	—	2	2	no	—
62	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
63	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
64	#107	C₂²×C₁₉	1	2	yes	—
65	#103	—	2	2	no	—
66	C₁₉	#2219	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×Q₈	—	2	2	no	—
68	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
69	Q₁₆	—	2	2	no	—
70	Q₁₆	—	2	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	4	2	no	—
77	C₂²⋊C₄	—	4	2	no	—
78	C₁₆	—	2	1	no	—
79	C₁₆	D₄×C₁₉	1	2	yes	—
80	C₂³	D₈×C₁₉	1	1	yes	characteristic
81	Q₈	—	4	2	no	—
82	Q₈	—	4	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	4	2	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	D₈×C₁₉	1	1	yes	characteristic
88	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
91	C₈	#41×C₁₉	1	1	yes	characteristic
92	C₂²	—	2	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	C₂×D₈×C₁₉	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	2	no	—
97	C₄	—	8	2	no	—
98	C₄	C₁₉×#121	1	1	yes	characteristic
99	C₄	C₁₉×#135	1	1	yes	characteristic
100	C₂	—	4	1	no	—
101	C₂	C₁₉×#466	1	1	yes	characteristic
102	C₂	C₁₉×#510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×M₃₂

C₂

yes

maximal, characteristic

C₁₉×#467

C₂

yes

maximal

C₁₉×#367

C₂

yes

maximal, characteristic, complemented

C₁₉×#358

C₂

yes

maximal, complemented

C₂×Q₁₆×C₁₉

C₂²

yes

—

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#107

C₂²

yes

—

C₁₉×#103

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

D₄

yes

—

C₂³×C₁₉

D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂×D₄

yes

C₈×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂×M₃₂

C₂×C₁₉

yes

characteristic

#467

C₂×C₁₉

yes

—

#367

C₂×C₁₉

yes

characteristic, complemented

#358

C₂×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

#466

yes

characteristic

C₂×C₁₉

#510

yes

—

C₂×Q₁₆

C₂²×C₁₉

yes

—

C₂²×C₈

C₂²×C₁₉

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#107

C₂²×C₁₉

yes

—

#103

—

C₁₉

#2219

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₁₆

D₄×C₁₉

yes

—

C₂³

D₈×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₈×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

C₂×D₄×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₂×D₈×C₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₁₉×#121

yes

characteristic

C₄

C₁₉×#135

yes

characteristic

100

C₂

—

101

C₂

C₁₉×#466

yes

characteristic

102

C₂

C₁₉×#510

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₂³×C₁₉

D₈

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×Q₃₂	C₂	semidirect
4. C₁₉×#367	C₂	semidirect
5. C₁₉×#358	C₂	semidirect
40. #2219	C₁₉	direct (N × H)
49. C₂×Q₃₂	C₂×C₁₉	semidirect
52. #367	C₂×C₁₉	semidirect
53. #358	C₂×C₁₉	semidirect
66. C₁₉	#2219	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×Q₃₂

C₂

semidirect

4. C₁₉×#367

C₂

semidirect

5. C₁₉×#358

C₂

semidirect

40. #2219

C₁₉

direct (N × H)

49. C₂×Q₃₂

C₂×C₁₉

semidirect

52. #367

C₂×C₁₉

semidirect

53. #358

C₂×C₁₉

semidirect

66. C₁₉

#2219

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
C₂×C₁₉×M₃₂	2
C₁₉×#467	2
C₁₉×#367	2
C₁₉×#358	2
#2219	19

subgroup

index

C₂×C₁₉×Q₃₂

C₂×C₁₉×M₃₂

C₁₉×#467

C₁₉×#367

C₁₉×#358

#2219

Subgroups — C₁₉×#2219 #14560076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2219 #14560076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2219 #14560076