Group #14559553 — subgroups

Subgroups — C₁₉×#1696 #14559553

Order 2432.

140 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 68 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	C₁₉×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#477	C₂	1	2	yes	maximal
3	C₁₉×#446	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#334	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#333	C₂	1	2	yes	maximal
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#107	—	2	1	no	—
9	C₁₉×#107	—	2	1	no	—
10	C₁₉×#107	—	2	2	no	—
11	C₁₉×C₄⋊C₈	—	2	1	no	—
12	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₁₉×#103	—	2	2	no	—
15	C₁₉×#97	—	2	1	no	—
16	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₉	—	2	2	no	—
18	C₂×Q₈×C₁₉	D₄	1	1	yes	characteristic
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	—	2	2	no	—
21	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₉	—	2	1	no	—
24	C₄⋊C₄×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
27	C₄²×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	Q₈×C₁₉	—	2	2	no	—
30	Q₈×C₁₉	—	8	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	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	—	4	1	no	—
39	C₈×C₁₉	—	4	2	no	—
40	C₈×C₁₉	Q₁₆	1	2	yes	—
41	#1696	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₁₉	#121	1	1	yes	characteristic
43	C₄×C₁₉	—	2	1	no	—
44	C₄×C₁₉	—	4	1	no	—
45	C₄×C₁₉	—	4	1	no	—
46	C₄×C₁₉	—	8	2	no	—
47	C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
48	C₄×C₁₉	#137	1	1	yes	characteristic
49	C₄×C₁₉	#137	1	2	yes	—
50	#500	C₂×C₁₉	1	1	yes	characteristic
51	#477	C₂×C₁₉	1	2	yes	—
52	#446	C₂×C₁₉	1	1	yes	characteristic
53	#334	C₂×C₁₉	1	1	yes	characteristic
54	#333	C₂×C₁₉	1	2	yes	—
55	C₂×C₁₉	#462	1	1	yes	characteristic
56	C₂×C₁₉	#470	1	1	yes	characteristic
57	C₂×C₁₉	#472	1	1	yes	characteristic
58	C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
59	C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
60	#107	—	2	1	no	—
61	#107	—	2	1	no	—
62	#107	—	2	2	no	—
63	C₄⋊C₈	—	2	1	no	—
64	C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
65	C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
66	#103	—	2	2	no	—
67	#97	—	2	1	no	—
68	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
69	C₁₉	#1696	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×Q₈	—	2	2	no	—
71	C₂×Q₈	D₄×C₁₉	1	1	yes	characteristic
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
75	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
76	C₄⋊C₄	—	2	1	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	2	2	no	—
79	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
80	C₄²	—	2	1	no	—
81	C₄²	C₂³×C₁₉	1	1	yes	characteristic
82	Q₈	—	2	2	no	—
83	Q₈	—	8	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
88	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
89	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	4	1	no	—
92	C₈	—	4	2	no	—
93	C₈	Q₁₆×C₁₉	1	2	yes	—
94	C₂²	C₁₉×#121	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	4	1	no	—
97	C₄	—	4	1	no	—
98	C₄	—	8	2	no	—
99	C₄	C₂×Q₁₆×C₁₉	1	1	yes	characteristic
100	C₄	C₁₉×#137	1	1	yes	characteristic
101	C₄	C₁₉×#137	1	2	yes	—
102	C₂	C₁₉×#462	1	1	yes	characteristic
103	C₂	C₁₉×#470	1	1	yes	characteristic
104	C₂	C₁₉×#472	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#500

C₂

yes

maximal, characteristic

C₁₉×#477

C₂

yes

maximal

C₁₉×#446

C₂

yes

maximal, characteristic

C₁₉×#334

C₂

yes

maximal, characteristic

C₁₉×#333

C₂

yes

maximal

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₄×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₁₉×C₄⋊C₈

C₂²

yes

—

C₁₉×#103

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄²×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

Q₁₆

yes

—

#1696

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

#121

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×Q₁₆

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#500

C₂×C₁₉

yes

characteristic

#477

C₂×C₁₉

yes

—

#446

C₂×C₁₉

yes

characteristic

#334

C₂×C₁₉

yes

characteristic

#333

C₂×C₁₉

yes

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₄⋊Q₈

C₂²×C₁₉

yes

—

C₄×Q₈

C₂²×C₁₉

yes

—

—

—

C₄⋊C₈

—

C₄⋊C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₈

C₂²×C₁₉

yes

—

#103

—

#97

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#1696

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

D₄×C₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₁₉

yes

characteristic

C₄²

—

C₄²

C₂³×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₂×C₄

#41×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

Q₁₆×C₁₉

yes

—

C₂²

C₁₉×#121

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

C₂×Q₁₆×C₁₉

yes

characteristic

100

C₄

C₁₉×#137

yes

characteristic

101

C₄

C₁₉×#137

yes

—

102

C₂

C₁₉×#462

yes

characteristic

103

C₂

C₁₉×#470

yes

characteristic

104

C₂

C₁₉×#472

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₁₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

#121

commutator, Frattini, cosocle

C₄²

C₂³×C₁₉

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
41. #1696	C₁₉	direct (N × H)
69. C₁₉	#1696	direct (N × H)

H ≅ G/N

type

41. #1696

C₁₉

direct (N × H)

69. C₁₉

#1696

direct (N × H)

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

subgroup	index
C₁₉×#500	2
C₁₉×#477	2
C₁₉×#446	2
C₁₉×#334	2
C₁₉×#333	2
#1696	19

subgroup

index

C₁₉×#500

C₁₉×#477

C₁₉×#446

C₁₉×#334

C₁₉×#333

#1696

Subgroups — C₁₉×#1696 #14559553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1696 #14559553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1696 #14559553