Group #14560035 — subgroups

Subgroups — C₁₉×#2178 #14560035

Order 2432.

146 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 76 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×#508	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#443	C₂	1	2	yes	maximal, complemented
3	C₁₉×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#359	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#135	C₂²	1	2	yes	—
7	C₁₉×#131	—	2	2	no	—
8	C₁₉×Q₃₂	C₄	1	1	yes	characteristic, complemented
9	C₁₉×SD₃₂	C₄	1	2	yes	complemented
10	C₁₉×D₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₁₉×#108	C₂²	1	2	yes	—
14	C₁₉×#104	—	2	2	no	—
15	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
16	#41×C₁₉	—	2	2	no	—
17	Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
18	SD₁₆×C₁₉	—	2	2	no	—
19	D₈×C₁₉	C₂×C₄	1	2	yes	—
20	M₁₆×C₁₉	—	2	2	no	—
21	M₁₆×C₁₉	—	4	2	no	—
22	C₂×C₈×C₁₉	—	4	2	no	—
23	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
25	C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₁₆×C₁₉	—	2	1	no	—
27	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
29	Q₈×C₁₉	—	2	2	no	—
30	D₄×C₁₉	—	2	2	no	—
31	D₄×C₁₉	—	4	2	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	C₈×C₁₉	—	4	2	no	—
36	C₈×C₁₉	D₈	1	1	yes	characteristic
37	C₈×C₁₉	D₈	1	1	yes	characteristic
38	C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
39	C₈×C₁₉	#41	1	1	yes	characteristic
40	#2178	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₁₉	—	4	2	no	—
42	C₂²×C₁₉	#135	1	1	yes	characteristic
43	C₄×C₁₉	—	2	2	no	—
44	C₄×C₁₉	—	4	2	no	—
45	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
46	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
47	#508	C₂×C₁₉	1	1	yes	characteristic
48	#443	C₂×C₁₉	1	2	yes	complemented
49	#368	C₂×C₁₉	1	1	yes	characteristic, complemented
50	#359	C₂×C₁₉	1	2	yes	complemented
51	C₄×C₁₆	C₂×C₁₉	1	1	yes	characteristic, complemented
52	C₂×C₁₉	—	2	1	no	—
53	C₂×C₁₉	—	8	2	no	—
54	C₂×C₁₉	C₄×D₈	1	1	yes	characteristic
55	#135	C₂²×C₁₉	1	2	yes	—
56	#131	—	2	2	no	—
57	Q₃₂	C₄×C₁₉	1	1	yes	characteristic, complemented
58	SD₃₂	C₄×C₁₉	1	2	yes	complemented
59	D₁₆	C₄×C₁₉	1	1	yes	characteristic, complemented
60	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
61	C₂×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
62	#108	C₂²×C₁₉	1	2	yes	—
63	#104	—	2	2	no	—
64	C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
65	C₁₉	#2178	1	1	yes	characteristic, direct product factor, Sylow
66	#41	—	2	2	no	—
67	Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
68	SD₁₆	—	2	2	no	—
69	D₈	C₂×C₄×C₁₉	1	2	yes	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	4	2	no	—
72	C₂×C₈	—	4	2	no	—
73	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
74	C₂×C₈	C₂³×C₁₉	1	1	yes	characteristic
75	C₄²	D₄×C₁₉	1	1	yes	characteristic
76	C₁₆	—	2	1	no	—
77	C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
78	C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
79	Q₈	—	2	2	no	—
80	D₄	—	2	2	no	—
81	D₄	—	4	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
85	C₈	—	4	2	no	—
86	C₈	D₈×C₁₉	1	1	yes	characteristic
87	C₈	D₈×C₁₉	1	1	yes	characteristic
88	C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
89	C₈	#41×C₁₉	1	1	yes	characteristic
90	C₂²	—	4	2	no	—
91	C₂²	C₁₉×#135	1	1	yes	characteristic
92	C₄	—	2	2	no	—
93	C₄	—	4	2	no	—
94	C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
95	C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	8	2	no	—
98	C₂	C₄×D₈×C₁₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#508

C₂

yes

maximal, characteristic

C₁₉×#443

C₂

yes

maximal, complemented

C₁₉×#368

C₂

yes

maximal, characteristic, complemented

C₁₉×#359

C₂

yes

maximal, complemented

C₄×C₁₆×C₁₉

C₂

yes

maximal, characteristic, complemented

C₁₉×#135

C₂²

yes

—

C₁₉×#131

—

C₁₉×Q₃₂

C₄

yes

characteristic, complemented

C₁₉×SD₃₂

C₄

yes

complemented

C₁₉×D₁₆

C₄

yes

characteristic, complemented

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#108

C₂²

yes

—

C₁₉×#104

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#41×C₁₉

—

Q₁₆×C₁₉

C₂×C₄

yes

—

SD₁₆×C₁₉

—

D₈×C₁₉

C₂×C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

C₄²×C₁₉

D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₁₆×C₁₉

C₂×C₄

yes

characteristic

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

D₈

yes

characteristic

C₈×C₁₉

C₂²×C₄

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

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂×D₈

yes

characteristic

#508

C₂×C₁₉

yes

characteristic

#443

C₂×C₁₉

yes

complemented

#368

C₂×C₁₉

yes

characteristic, complemented

#359

C₂×C₁₉

yes

complemented

C₄×C₁₆

C₂×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

C₄×D₈

yes

characteristic

#135

C₂²×C₁₉

yes

—

#131

—

Q₃₂

C₄×C₁₉

yes

characteristic, complemented

SD₃₂

C₄×C₁₉

yes

complemented

D₁₆

C₄×C₁₉

yes

characteristic, complemented

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₆

C₂²×C₁₉

yes

characteristic

#108

C₂²×C₁₉

yes

—

#104

—

C₄×C₈

C₂²×C₁₉

yes

characteristic

C₁₉

#2178

yes

characteristic, direct product factor, Sylow

#41

—

Q₁₆

C₂×C₄×C₁₉

yes

—

SD₁₆

—

D₈

C₂×C₄×C₁₉

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

C₂³×C₁₉

yes

characteristic

C₄²

D₄×C₁₉

yes

characteristic

C₁₆

—

C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₁₆

C₂×C₄×C₁₉

yes

characteristic

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

C₈

—

C₈

D₈×C₁₉

yes

characteristic

C₈

D₈×C₁₉

yes

characteristic

C₈

C₂²×C₄×C₁₉

yes

characteristic

C₈

#41×C₁₉

yes

characteristic

C₂²

—

C₂²

C₁₉×#135

yes

characteristic

C₄

—

C₄

—

C₄

C₄×D₄×C₁₉

yes

characteristic

C₄

C₂×D₈×C₁₉

yes

characteristic

C₂

—

C₂

—

C₂

C₄×D₈×C₁₉

yes

characteristic

	subgroup	G/H
center	C₈×C₁₉	D₈
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₄×D₈
prime radical	C₁₉×#508	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₈×C₁₉

D₈

commutator

C₈

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₈

C₂³×C₁₉

socle

C₂×C₁₉

C₄×D₈

prime radical

C₁₉×#508

C₂

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#443	C₂	semidirect
3. C₁₉×#368	C₂	semidirect
4. C₁₉×#359	C₂	semidirect
5. C₄×C₁₆×C₁₉	C₂	semidirect
8. C₁₉×Q₃₂	C₄	semidirect
9. C₁₉×SD₃₂	C₄	semidirect
10. C₁₉×D₁₆	C₄	semidirect
40. #2178	C₁₉	direct (N × H)
48. #443	C₂×C₁₉	semidirect
49. #368	C₂×C₁₉	semidirect
50. #359	C₂×C₁₉	semidirect
51. C₄×C₁₆	C₂×C₁₉	semidirect
57. Q₃₂	C₄×C₁₉	semidirect
58. SD₃₂	C₄×C₁₉	semidirect
59. D₁₆	C₄×C₁₉	semidirect
65. C₁₉	#2178	direct (N × H)

H ≅ G/N

type

2. C₁₉×#443

C₂

semidirect

3. C₁₉×#368

C₂

semidirect

4. C₁₉×#359

C₂

semidirect

5. C₄×C₁₆×C₁₉

C₂

semidirect

8. C₁₉×Q₃₂

C₄

semidirect

9. C₁₉×SD₃₂

C₄

semidirect

10. C₁₉×D₁₆

C₄

semidirect

40. #2178

C₁₉

direct (N × H)

48. #443

C₂×C₁₉

semidirect

49. #368

C₂×C₁₉

semidirect

50. #359

C₂×C₁₉

semidirect

51. C₄×C₁₆

C₂×C₁₉

semidirect

57. Q₃₂

C₄×C₁₉

semidirect

58. SD₃₂

C₄×C₁₉

semidirect

59. D₁₆

C₄×C₁₉

semidirect

65. C₁₉

#2178

direct (N × H)

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

subgroup	index
C₁₉×#508	2
C₁₉×#443	2
C₁₉×#368	2
C₁₉×#359	2
C₄×C₁₆×C₁₉	2
#2178	19

subgroup

index

C₁₉×#508

C₁₉×#443

C₁₉×#368

C₁₉×#359

C₄×C₁₆×C₁₉

#2178

Subgroups — C₁₉×#2178 #14560035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#2178 #14560035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#2178 #14560035