Group #14569578 — subgroups

Subgroups — #14569578

Order 2432.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#10597320	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597316	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926462	C₂	1	8	yes	maximal, complemented
4	#11926446	C₂	1	4	yes	maximal, complemented
5	C₁₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	2	yes	—
7	C₂²×D₇₆	C₂²	1	4	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	16	yes	—
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×Dic₁₉⋊C₄	C₂²	1	4	yes	—
13	#10597320	—	2	4	no	—
14	#10597316	—	2	4	no	—
15	C₁₉×#95	C₂²	1	4	yes	—
16	C₂³×D₁₉	C₂³	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	C₂²×Dic₁₉	C₂³	1	4	yes	—
21	C₂×D₇₆	—	2	8	no	—
22	C₂×D₇₆	—	2	4	no	—
23	C₂×D₇₆	—	2	8	no	—
24	C₂×D₇₆	—	4	8	no	—
25	C₄²×C₁₉	—	2	4	no	—
26	C₄²×C₁₉	D₄	1	4	yes	—
27	(C₂×D₁₉)⋊C₄	—	4	16	no	—
28	C₄⋊Dic₁₉	—	2	4	no	—
29	Dic₁₉⋊C₄	—	2	8	no	—
30	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
31	C₂²×D₁₉	—	2	4	no	—
32	C₂²×D₁₉	—	2	8	no	—
33	C₂²×D₁₉	—	2	16	no	—
34	C₂×C₄×C₁₉	—	2	4	no	—
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	—	2	8	no	—
37	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
38	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₁₉	#41	1	4	yes	—
40	C₂×Dic₁₉	—	2	4	no	—
41	C₂×Dic₁₉	—	2	8	no	—
42	D₇₆	—	4	16	no	—
43	D₇₆	—	4	8	no	—
44	#2641	—	19	1	no	maximal, Sylow
45	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
46	C₂²×C₁₉	C₂×#41	1	2	yes	—
47	C₂²×C₁₉	H(5,𝔽₂)	1	4	yes	—
48	C₂×D₁₉	—	4	4	no	—
49	C₂×D₁₉	—	4	8	no	—
50	C₂×D₁₉	—	4	16	no	—
51	C₄×C₁₉	—	2	4	no	—
52	C₄×C₁₉	—	4	4	no	—
53	C₄×C₁₉	#124	1	4	yes	—
54	Dic₁₉	—	4	4	no	—
55	C₂×#127	—	19	1	no	—
56	C₂×#125	—	19	1	no	—
57	#394	—	19	8	no	—
58	#390	—	19	4	no	—
59	#376	D₁₉	1	1	yes	characteristic, complemented
60	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
61	C₂×C₁₉	#535	1	2	yes	—
62	C₂×C₁₉	#540	1	4	yes	—
63	D₁₉	—	8	4	no	—
64	C₂²×D₄	—	19	2	no	—
65	C₂²×D₄	—	19	4	no	—
66	#127	—	38	4	no	—
67	#125	—	38	4	no	—
68	C₂×C₄⋊C₄	—	19	2	no	—
69	C₂×C₄⋊C₄	—	19	4	no	—
70	C₂×C₂²⋊C₄	—	19	16	no	—
71	C₂×C₄²	C₂×D₁₉	1	2	yes	—
72	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
73	#95	C₂×D₁₉	1	4	yes	—
74	C₁₉	#2641	1	1	yes	characteristic, complemented, Sylow
75	C₂⁴	—	19	4	no	—
76	C₂×D₄	—	38	8	no	—
77	C₂×D₄	—	38	4	no	—
78	C₂×D₄	—	38	8	no	—
79	C₂×D₄	—	76	8	no	—
80	C₂²×C₄	—	19	4	no	—
81	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
82	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
83	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
84	C₄⋊C₄	—	38	8	no	—
85	C₄⋊C₄	—	38	4	no	—
86	C₂²⋊C₄	—	76	16	no	—
87	C₄²	—	2	4	no	—
88	C₄²	D₇₆	1	4	yes	—
89	C₂³	—	38	4	no	—
90	C₂³	—	38	8	no	—
91	C₂³	—	38	16	no	—
92	C₂³	C₂³×D₁₉	1	1	yes	characteristic
93	D₄	—	76	16	no	—
94	D₄	—	76	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	8	no	—
98	C₂×C₄	—	38	4	no	—
99	C₂×C₄	—	38	8	no	—
100	C₂×C₄	C₂×D₇₆	1	4	yes	—
101	C₂×C₄	C₂×D₇₆	1	2	yes	—
102	C₂×C₄	#64541	1	4	yes	—
103	C₂²	—	76	4	no	—
104	C₂²	—	76	8	no	—
105	C₂²	—	76	16	no	—
106	C₂²	C₂²×D₇₆	1	1	yes	characteristic
107	C₂²	C₂×#64541	1	2	yes	—
108	C₂²	#10597435	1	4	yes	—
109	C₄	—	2	4	no	—
110	C₄	—	4	4	no	—
111	C₄	—	76	4	no	—
112	C₄	#10597321	1	4	yes	—
113	C₂	—	152	4	no	—
114	C₂	C₂×#10597321	1	1	yes	characteristic
115	C₂	#11927113	1	2	yes	—
116	C₂	#11927149	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic

C₂×#10597316

C₂

yes

maximal, characteristic, complemented

#11926462

C₂

yes

maximal, complemented

#11926446

C₂

yes

maximal, complemented

C₁₉×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597320

—

#10597316

—

C₁₉×#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄²×C₁₉

—

C₄²×C₁₉

D₄

yes

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

#41

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

#2641

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂×#41

yes

—

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

C₂×#124

yes

characteristic

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#540

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

#127

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

C₂×D₁₉

yes

—

C₁₉

#2641

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

D₇₆

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₇₆

yes

—

101

C₂×C₄

C₂×D₇₆

yes

—

102

C₂×C₄

#64541

yes

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²×D₇₆

yes

characteristic

107

C₂²

C₂×#64541

yes

—

108

C₂²

#10597435

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

#10597321

yes

—

113

C₂

—

152

—

114

C₂

C₂×#10597321

yes

characteristic

115

C₂

#11927113

yes

—

116

C₂

#11927149

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#376	C₂
prime radical	C₂×#10597320	C₂
hypercenter	#376	D₁₉
hypocenter	C₁₉	#2641
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#376

C₂

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
2. C₂×#10597316	C₂	semidirect
3. #11926462	C₂	semidirect
4. #11926446	C₂	semidirect
5. C₁₉×#376	C₂	semidirect
59. #376	D₁₉	semidirect
74. C₁₉	#2641	semidirect

H ≅ G/N

type

2. C₂×#10597316

C₂

semidirect

3. #11926462

C₂

semidirect

4. #11926446

C₂

semidirect

5. C₁₉×#376

C₂

semidirect

59. #376

D₁₉

semidirect

74. C₁₉

#2641

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597316	2
#11926462	2
#11926446	2
C₁₉×#376	2
#2641	19

subgroup

index

C₁₉×#376

Subgroups — #14569578

Conjugacy classes of subgroups

Complements

Maximal subgroups