Group #14559248 — subgroups

Subgroups — C₁₉×#1391 #14559248

Order 2432.

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

normal subgroups only

This group has 166 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	C₁₉×#410	C₂	1	2	yes	maximal
2	C₁₉×#408	C₂	1	1	yes	maximal, characteristic
3	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
4	C₂×M₁₆×C₁₉	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₈×C₁₉	C₄	1	1	yes	characteristic, complemented
6	C₁₉×#117	—	2	2	no	—
7	C₁₉×#99	—	2	2	no	—
8	C₁₉×#99	C₄	1	4	yes	complemented
9	C₁₉×C₂²⋊C₈	—	2	2	no	—
10	#41×C₁₉	—	4	1	no	—
11	#41×C₁₉	—	4	1	no	—
12	C₂×Q₈×C₁₉	Q₈	1	1	yes	characteristic
13	C₂×D₄×C₁₉	C₂×C₄	1	2	yes	—
14	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	D₄	1	2	yes	—
17	M₁₆×C₁₉	—	4	1	no	—
18	C₂×C₈×C₁₉	—	2	1	no	—
19	C₂×C₈×C₁₉	—	2	1	no	—
20	C₂×C₈×C₁₉	—	4	1	no	—
21	C₄⋊C₄×C₁₉	—	4	2	no	—
22	C₂²⋊C₄×C₁₉	—	2	4	no	—
23	C₄²×C₁₉	—	4	2	no	—
24	C₂³×C₁₉	C₄²	1	1	yes	characteristic
25	C₂³×C₁₉	C₂²⋊C₄	1	2	yes	—
26	Q₈×C₁₉	—	4	1	no	—
27	D₄×C₁₉	—	4	2	no	—
28	D₄×C₁₉	—	4	1	no	—
29	C₂×C₄×C₁₉	—	2	2	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	2	2	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	4	no	—
34	C₂×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
37	C₈×C₁₉	—	4	1	no	—
38	C₈×C₁₉	—	4	1	no	—
39	#1391	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₁₉	—	2	2	no	—
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	4	1	no	—
43	C₂²×C₁₉	—	4	2	no	—
44	C₂²×C₁₉	#95	1	1	yes	characteristic
45	C₄×C₁₉	—	2	2	no	—
46	C₄×C₁₉	—	2	1	no	—
47	C₄×C₁₉	—	8	4	no	—
48	C₄×C₁₉	#99	1	1	yes	characteristic
49	C₄×C₁₉	#99	1	1	yes	characteristic
50	#410	C₂×C₁₉	1	2	yes	—
51	#408	C₂×C₁₉	1	1	yes	characteristic
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	4	2	no	—
54	C₂×C₁₉	—	4	1	no	—
55	C₂×C₁₉	#342	1	1	yes	characteristic
56	C₂×#41	C₂²×C₁₉	1	1	yes	characteristic
57	C₂×M₁₆	C₄×C₁₉	1	1	yes	characteristic, complemented
58	C₂²×C₈	C₄×C₁₉	1	1	yes	characteristic, complemented
59	#117	—	2	2	no	—
60	#99	—	2	2	no	—
61	#99	C₄×C₁₉	1	4	yes	complemented
62	C₂²⋊C₈	—	2	2	no	—
63	C₁₉	#1391	1	1	yes	characteristic, direct product factor, Sylow
64	#41	—	4	1	no	—
65	#41	—	4	1	no	—
66	C₂×Q₈	Q₈×C₁₉	1	1	yes	characteristic
67	C₂×D₄	C₂×C₄×C₁₉	1	2	yes	—
68	C₂×D₄	D₄×C₁₉	1	1	yes	characteristic
69	C₂²×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
70	C₂²×C₄	D₄×C₁₉	1	2	yes	—
71	M₁₆	—	4	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	4	1	no	—
75	C₄⋊C₄	—	4	2	no	—
76	C₂²⋊C₄	—	2	4	no	—
77	C₄²	—	4	2	no	—
78	C₂³	C₄²×C₁₉	1	1	yes	characteristic
79	C₂³	C₂²⋊C₄×C₁₉	1	2	yes	—
80	Q₈	—	4	1	no	—
81	D₄	—	4	2	no	—
82	D₄	—	4	1	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	4	no	—
88	C₂×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
89	C₂×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
90	C₂×C₄	C₄⋊C₄×C₁₉	1	2	yes	—
91	C₈	—	4	1	no	—
92	C₈	—	4	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	4	1	no	—
96	C₂²	—	4	2	no	—
97	C₂²	C₁₉×#95	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	—	8	4	no	—
101	C₄	C₁₉×#99	1	1	yes	characteristic
102	C₄	C₁₉×#99	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	4	2	no	—
105	C₂	—	4	1	no	—
106	C₂	C₁₉×#342	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#410

C₂

yes

maximal

C₁₉×#408

C₂

yes

maximal, characteristic

C₂×#41×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

C₄

yes

characteristic, complemented

C₂²×C₈×C₁₉

C₄

yes

characteristic, complemented

C₁₉×#117

—

C₁₉×#99

—

C₁₉×#99

C₄

yes

complemented

C₁₉×C₂²⋊C₈

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

Q₈

yes

characteristic

C₂×D₄×C₁₉

C₂×C₄

yes

—

C₂×D₄×C₁₉

D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂³×C₁₉

C₄²

yes

characteristic

C₂³×C₁₉

C₂²⋊C₄

yes

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₄

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1391

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#95

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

—

#408

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#342

yes

characteristic

C₂×#41

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

C₄×C₁₉

yes

characteristic, complemented

C₂²×C₈

C₄×C₁₉

yes

characteristic, complemented

#117

—

#99

—

#99

C₄×C₁₉

yes

complemented

C₂²⋊C₈

—

C₁₉

#1391

yes

characteristic, direct product factor, Sylow

#41

—

#41

—

C₂×Q₈

Q₈×C₁₉

yes

characteristic

C₂×D₄

C₂×C₄×C₁₉

yes

—

C₂×D₄

D₄×C₁₉

yes

characteristic

C₂²×C₄

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₄

D₄×C₁₉

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

C₄²×C₁₉

yes

characteristic

C₂³

C₂²⋊C₄×C₁₉

yes

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₄

C₄⋊C₄×C₁₉

yes

characteristic

C₂×C₄

C₄⋊C₄×C₁₉

yes

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₉×#95

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

C₁₉×#99

yes

characteristic

102

C₄

C₁₉×#99

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

—

106

C₂

C₁₉×#342

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#99
commutator	C₂³	C₄²×C₁₉
Frattini, cosocle	C₂×#41	C₂²×C₁₉
socle	C₂×C₁₉	#342
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

subgroup

G/H

center

C₄×C₁₉

#99

commutator

C₂³

C₄²×C₁₉

Frattini, cosocle

C₂×#41

C₂²×C₁₉

socle

C₂×C₁₉

#342

prime radical

C₂×#41×C₁₉

C₂²

LCS

G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

N	H ≅ G/N	type
4. C₂×M₁₆×C₁₉	C₄	semidirect
5. C₂²×C₈×C₁₉	C₄	semidirect
8. C₁₉×#99	C₄	semidirect
39. #1391	C₁₉	direct (N × H)
57. C₂×M₁₆	C₄×C₁₉	semidirect
58. C₂²×C₈	C₄×C₁₉	semidirect
61. #99	C₄×C₁₉	semidirect
63. C₁₉	#1391	direct (N × H)

H ≅ G/N

type

4. C₂×M₁₆×C₁₉

C₄

semidirect

5. C₂²×C₈×C₁₉

C₄

semidirect

8. C₁₉×#99

C₄

semidirect

39. #1391

C₁₉

direct (N × H)

57. C₂×M₁₆

C₄×C₁₉

semidirect

58. C₂²×C₈

C₄×C₁₉

semidirect

61. #99

C₄×C₁₉

semidirect

63. C₁₉

#1391

direct (N × H)

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

subgroup	index
C₁₉×#410	2
C₁₉×#408	2
#1391	19

subgroup

index

C₁₉×#410

C₁₉×#408

#1391

Subgroups — C₁₉×#1391 #14559248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1391 #14559248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1391 #14559248