Group #14560096 — subgroups

Subgroups — C₁₉×#2239 #14560096

Order 2432.

124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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×#470	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#430	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#365	C₂	1	2	yes	maximal, complemented
4	C₁₉×#362	C₂	1	2	yes	maximal, complemented
5	C₁₉×#349	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₁₉	—	2	1	no	—
8	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×C₂²⋊Q₈	—	2	1	no	—
10	C₁₉×M₃₂	C₂²	1	2	yes	—
11	C₁₉×#108	—	2	1	no	—
12	C₁₉×#108	C₂²	1	2	yes	—
13	C₁₉×#106	C₂²	1	1	yes	characteristic
14	C₁₉×#103	—	2	1	no	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
17	Q₁₆×C₁₉	—	2	2	no	—
18	M₁₆×C₁₉	—	2	2	no	—
19	M₁₆×C₁₉	—	2	2	no	—
20	M₁₆×C₁₉	—	4	1	no	—
21	C₂×C₈×C₁₉	—	4	1	no	—
22	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₁₉	—	2	1	no	—
25	C₄⋊C₄×C₁₉	—	4	1	no	—
26	C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
29	Q₈×C₁₉	—	4	1	no	—
30	Q₈×C₁₉	—	4	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	—	2	1	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	—	4	1	no	—
35	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
37	C₈×C₁₉	—	2	1	no	—
38	C₈×C₁₉	—	4	2	no	—
39	C₈×C₁₉	#41	1	2	yes	—
40	#2239	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	—	2	1	no	—
42	C₂²×C₁₉	—	4	1	no	—
43	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
44	C₄×C₁₉	—	2	1	no	—
45	C₄×C₁₉	—	8	1	no	—
46	C₄×C₁₉	—	8	1	no	—
47	C₄×C₁₉	#123	1	1	yes	characteristic
48	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
49	#470	C₂×C₁₉	1	1	yes	characteristic
50	#430	C₂×C₁₉	1	1	yes	characteristic
51	#365	C₂×C₁₉	1	2	yes	complemented
52	#362	C₂×C₁₉	1	2	yes	complemented
53	#349	C₂×C₁₉	1	1	yes	characteristic
54	C₂×C₁₉	—	2	1	no	—
55	C₂×C₁₉	—	4	1	no	—
56	C₂×C₁₉	#481	1	1	yes	characteristic
57	C₂×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
58	C₂×M₁₆	—	2	1	no	—
59	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
60	C₂²⋊Q₈	—	2	1	no	—
61	M₃₂	C₂²×C₁₉	1	2	yes	—
62	#108	—	2	1	no	—
63	#108	C₂²×C₁₉	1	2	yes	—
64	#106	C₂²×C₁₉	1	1	yes	characteristic
65	#103	—	2	1	no	—
66	C₁₉	#2239	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×Q₈	—	2	1	no	—
68	C₂²×C₄	D₄×C₁₉	1	1	yes	characteristic
69	Q₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	2	2	no	—
72	M₁₆	—	4	1	no	—
73	C₂×C₈	—	4	1	no	—
74	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
75	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
76	C₄⋊C₄	—	2	1	no	—
77	C₄⋊C₄	—	4	1	no	—
78	C₂²⋊C₄	—	4	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	SD₁₆×C₁₉	1	1	yes	characteristic
81	Q₈	—	4	1	no	—
82	Q₈	—	4	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	4	1	no	—
86	C₂×C₄	—	4	1	no	—
87	C₂×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
88	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	4	2	no	—
91	C₈	#41×C₁₉	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	8	1	no	—
97	C₄	—	8	1	no	—
98	C₄	C₁₉×#123	1	1	yes	characteristic
99	C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	C₁₉×#481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#470

C₂

yes

maximal, characteristic

C₁₉×#430

C₂

yes

maximal, characteristic

C₁₉×#365

C₂

yes

maximal, complemented

C₁₉×#362

C₂

yes

maximal, complemented

C₁₉×#349

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₁₉

C₂²

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

—

C₁₉×M₃₂

C₂²

yes

—

C₁₉×#108

—

C₁₉×#108

C₂²

yes

—

C₁₉×#106

C₂²

yes

characteristic

C₁₉×#103

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

characteristic

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×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

—

C₂³×C₁₉

SD₁₆

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

#2239

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×C₁₉

yes

characteristic

#430

C₂×C₁₉

yes

characteristic

#365

C₂×C₁₉

yes

complemented

#362

C₂×C₁₉

yes

complemented

#349

C₂×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

C₂×Q₁₆

C₂²×C₁₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

C₂²⋊Q₈

—

M₃₂

C₂²×C₁₉

yes

—

#108

—

#108

C₂²×C₁₉

yes

—

#106

C₂²×C₁₉

yes

characteristic

#103

—

C₁₉

#2239

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂²×C₄

D₄×C₁₉

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

SD₁₆×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

SD₁₆×C₁₉

yes

characteristic

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

—

C₈

#41×C₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂×SD₁₆×C₁₉

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

C₁₉×#123

yes

characteristic

C₄

C₁₉×AGL(1,ℤ/8)

yes

characteristic

100

C₂

—

101

C₂

—

102

C₂

C₁₉×#481

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#481
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#481

commutator, Frattini, cosocle

C₂×C₈

C₂³×C₁₉

prime radical

C₂³×C₁₉

SD₁₆

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×M₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#365	C₂	semidirect
4. C₁₉×#362	C₂	semidirect
40. #2239	C₁₉	direct (N × H)
51. #365	C₂×C₁₉	semidirect
52. #362	C₂×C₁₉	semidirect
66. C₁₉	#2239	direct (N × H)

H ≅ G/N

type

3. C₁₉×#365

C₂

semidirect

4. C₁₉×#362

C₂

semidirect

40. #2239

C₁₉

direct (N × H)

51. #365

C₂×C₁₉

semidirect

52. #362

C₂×C₁₉

semidirect

66. C₁₉

#2239

direct (N × H)

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

subgroup	index
C₁₉×#470	2
C₁₉×#430	2
C₁₉×#365	2
C₁₉×#362	2
C₁₉×#349	2
#2239	19

subgroup

index

C₁₉×#470

C₁₉×#430

C₁₉×#365

C₁₉×#362

C₁₉×#349

#2239

Subgroups — C₁₉×#2239 #14560096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2239 #14560096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2239 #14560096