Group #18038835 — subgroups

Subgroups — C₁₉×#32876 #18038835

Order 4864.

584 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 186 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×#2091	C₂	1	4	yes	maximal
2	C₁₉×#2070	C₂	1	8	yes	maximal, complemented
3	C₁₉×#1784	C₂	1	3	yes	maximal
4	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₁₉×#430	C₂²	1	12	yes	—
6	C₂×C₁₉×#101	C₂²	1	12	yes	—
7	C₁₉×#407	C₂²	1	6	yes	—
8	C₁₉×#338	C₂²	1	4	yes	—
9	C₂²×Q₈×C₁₉	—	4	6	no	—
10	C₂²×Q₈×C₁₉	Q₈	1	2	yes	—
11	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
12	C₂³×C₄×C₁₉	Q₈	1	2	yes	—
13	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×M₁₆×C₁₉	C₂³	1	12	yes	—
15	C₁₉×#108	—	4	12	no	—
16	C₁₉×#101	—	4	12	no	—
17	C₁₉×C₂²⋊C₈	—	4	6	no	—
18	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
19	C₂×Q₈×C₁₉	—	2	12	no	—
20	C₂×Q₈×C₁₉	—	4	6	no	—
21	C₂×Q₈×C₁₉	—	4	16	no	—
22	C₂²×C₄×C₁₉	—	2	6	no	—
23	C₂²×C₄×C₁₉	—	4	6	no	—
24	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
25	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
26	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
27	M₁₆×C₁₉	—	2	24	no	—
28	C₂×C₈×C₁₉	—	2	12	no	—
29	#32876	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₁₉	—	2	3	no	—
31	C₂³×C₁₉	—	4	2	no	—
32	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
33	Q₈×C₁₉	—	4	8	no	—
34	Q₈×C₁₉	—	4	8	no	—
35	C₂×C₄×C₁₉	—	2	3	no	—
36	C₂×C₄×C₁₉	—	2	12	no	—
37	C₂×C₄×C₁₉	—	4	8	no	—
38	C₂×C₄×C₁₉	—	4	4	no	—
39	C₂×C₄×C₁₉	H(5,𝔽₂)	1	6	yes	—
40	C₈×C₁₉	—	4	12	no	—
41	#2091	C₂×C₁₉	1	4	yes	—
42	#2070	C₂×C₁₉	1	8	yes	complemented
43	#1784	C₂×C₁₉	1	3	yes	—
44	C₂²×C₁₉	—	2	6	no	—
45	C₂²×C₁₉	—	4	1	no	—
46	C₂²×C₁₉	—	4	3	no	—
47	C₂²×C₁₉	—	4	1	no	—
48	C₂²×C₁₉	#543	1	3	yes	—
49	C₄×C₁₉	—	4	1	no	—
50	C₄×C₁₉	—	4	4	no	—
51	C₄×C₁₉	#560	1	4	yes	—
52	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
53	#430	C₂²×C₁₉	1	12	yes	—
54	C₂×#101	C₂²×C₁₉	1	12	yes	—
55	#407	C₂²×C₁₉	1	6	yes	—
56	#338	C₂²×C₁₉	1	4	yes	—
57	C₂×C₁₉	—	2	3	no	—
58	C₂×C₁₉	—	4	2	no	—
59	C₂×C₁₉	#2842	1	1	yes	characteristic
60	C₂²×Q₈	—	4	6	no	—
61	C₂²×Q₈	Q₈×C₁₉	1	2	yes	—
62	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
63	C₂³×C₄	Q₈×C₁₉	1	2	yes	—
64	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
65	C₂×M₁₆	C₂³×C₁₉	1	12	yes	—
66	#108	—	4	12	no	—
67	#101	—	4	12	no	—
68	C₂²⋊C₈	—	4	6	no	—
69	C₁₉	#32876	1	1	yes	characteristic, direct product factor, Sylow
70	C₂⁴	C₂×Q₈×C₁₉	1	1	yes	characteristic
71	C₂×Q₈	—	2	12	no	—
72	C₂×Q₈	—	4	6	no	—
73	C₂×Q₈	—	4	16	no	—
74	C₂²×C₄	—	2	6	no	—
75	C₂²×C₄	—	4	6	no	—
76	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
77	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
78	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
79	M₁₆	—	2	24	no	—
80	C₂×C₈	—	2	12	no	—
81	C₂³	—	2	3	no	—
82	C₂³	—	4	2	no	—
83	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
84	Q₈	—	4	8	no	—
85	Q₈	—	4	8	no	—
86	C₂×C₄	—	2	3	no	—
87	C₂×C₄	—	2	12	no	—
88	C₂×C₄	—	4	8	no	—
89	C₂×C₄	—	4	4	no	—
90	C₂×C₄	C₁₉×H(5,𝔽₂)	1	6	yes	—
91	C₈	—	4	12	no	—
92	C₂²	—	2	6	no	—
93	C₂²	—	4	1	no	—
94	C₂²	—	4	3	no	—
95	C₂²	—	4	1	no	—
96	C₂²	C₁₉×#543	1	3	yes	—
97	C₄	—	4	1	no	—
98	C₄	—	4	4	no	—
99	C₄	C₁₉×#560	1	4	yes	—
100	C₂	—	2	3	no	—
101	C₂	—	4	2	no	—
102	C₂	C₁₉×#2842	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2091

C₂

yes

maximal

C₁₉×#2070

C₂

yes

maximal, complemented

C₁₉×#1784

C₂

yes

maximal

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₁₉×#430

C₂²

yes

—

C₂×C₁₉×#101

C₂²

yes

—

C₁₉×#407

C₂²

yes

—

C₁₉×#338

C₂²

yes

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

Q₈

yes

—

C₂²×Q₈×C₁₉

C₂³

yes

—

C₂³×C₄×C₁₉

Q₈

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

C₂³

yes

—

C₁₉×#108

—

C₁₉×#101

—

C₁₉×C₂²⋊C₈

—

C₂⁴×C₁₉

C₂×Q₈

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

—

C₂²×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂²×C₄×C₁₉

C₂⁴

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

#32876

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×Q₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

H(5,𝔽₂)

yes

—

C₈×C₁₉

—

#2091

C₂×C₁₉

yes

—

#2070

C₂×C₁₉

yes

complemented

#1784

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#543

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#560

yes

—

C₂³×Q₈

C₂²×C₁₉

yes

characteristic

#430

C₂²×C₁₉

yes

—

C₂×#101

C₂²×C₁₉

yes

—

#407

C₂²×C₁₉

yes

—

#338

C₂²×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2842

yes

characteristic

C₂²×Q₈

—

C₂²×Q₈

Q₈×C₁₉

yes

—

C₂²×Q₈

C₂³×C₁₉

yes

—

C₂³×C₄

Q₈×C₁₉

yes

—

C₂³×C₄

C₂³×C₁₉

yes

characteristic

C₂×M₁₆

C₂³×C₁₉

yes

—

#108

—

#101

—

C₂²⋊C₈

—

C₁₉

#32876

yes

characteristic, direct product factor, Sylow

C₂⁴

C₂×Q₈×C₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Q₈×C₁₉

yes

—

C₂²×C₄

C₂×Q₈×C₁₉

yes

characteristic

C₂²×C₄

C₂⁴×C₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂³

—

C₂³

—

C₂³

C₂²×Q₈×C₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₁₉×H(5,𝔽₂)

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₁₉×#543

yes

—

C₄

—

C₄

—

C₄

C₁₉×#560

yes

—

100

C₂

—

101

C₂

—

102

C₂

C₁₉×#2842

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2842
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#2842

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₉

prime radical

C₂⁴×C₁₉

C₂×Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2070	C₂	semidirect
29. #32876	C₁₉	direct (N × H)
42. #2070	C₂×C₁₉	semidirect
69. C₁₉	#32876	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2070

C₂

semidirect

29. #32876

C₁₉

direct (N × H)

42. #2070

C₂×C₁₉

semidirect

69. C₁₉

#32876

direct (N × H)

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

subgroup	index
C₁₉×#2091	2
C₁₉×#2070	2
C₁₉×#1784	2
#32876	19

subgroup

index

C₁₉×#2091

C₁₉×#2070

C₁₉×#1784

#32876

Subgroups — C₁₉×#32876 #18038835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#32876 #18038835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32876 #18038835