Group #14571678 — subgroups

Subgroups — #14571678

Order 2432.

630 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2	C₂×#10597322	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926462	C₂	1	6	yes	maximal, complemented
4	#11926454	C₂	1	6	yes	maximal, complemented
5	C₁₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₇₆	C₂²	1	6	yes	—
7	C₂²×D₇₆	C₂²	1	4	yes	—
8	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	—
10	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	12	yes	—
11	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	—
12	#10597322	—	2	4	no	—
13	#10597320	—	2	4	no	—
14	C₁₉×#95	C₂²	1	6	yes	—
15	C₂³×D₁₉	C₂³	1	1	yes	characteristic
16	C₂³×D₁₉	C₂³	1	4	yes	—
17	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
18	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
19	C₂²×Dic₁₉	C₂³	1	3	yes	—
20	C₂×D₇₆	—	2	12	no	—
21	C₂×D₇₆	—	4	12	no	—
22	C₂×D₇₆	—	4	12	no	—
23	C₄²×C₁₉	D₄	1	4	yes	complemented
24	(C₂×D₁₉)⋊C₄	—	2	6	no	—
25	(C₂×D₁₉)⋊C₄	—	4	12	no	—
26	Dic₁₉⋊C₄	—	2	6	no	—
27	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
28	C₂²×D₁₉	—	2	1	no	—
29	C₂²×D₁₉	—	2	4	no	—
30	C₂²×D₁₉	—	2	12	no	—
31	C₂²×D₁₉	—	2	12	no	—
32	C₂²×D₁₉	—	2	6	no	—
33	C₂×C₄×C₁₉	—	2	6	no	—
34	C₂×C₄×C₁₉	—	2	12	no	—
35	C₂×C₄×C₁₉	C₂×D₄	1	6	yes	—
36	C₂×Dic₁₉	—	2	3	no	—
37	C₂×Dic₁₉	—	2	6	no	—
38	D₇₆	—	4	24	no	—
39	D₇₆	—	4	16	no	—
40	#2818	—	19	1	no	maximal, Sylow
41	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
42	C₂²×C₁₉	H(5,𝔽₂)	1	6	yes	—
43	C₂×D₁₉	—	4	12	no	—
44	C₂×D₁₉	—	4	3	no	—
45	C₂×D₁₉	—	4	4	no	—
46	C₂×D₁₉	—	4	4	no	—
47	C₂×D₁₉	—	4	12	no	—
48	C₄×C₁₉	—	2	6	no	—
49	C₄×C₁₉	—	4	4	no	—
50	Dic₁₉	—	4	3	no	—
51	C₂×#127	—	19	1	no	—
52	C₂×#126	—	19	1	no	—
53	#394	—	19	6	no	—
54	#392	—	19	6	no	—
55	#383	D₁₉	1	1	yes	characteristic, complemented
56	C₂×C₁₉	#535	1	3	yes	—
57	C₂×C₁₉	#560	1	4	yes	—
58	D₁₉	—	8	4	no	—
59	D₁₉	—	8	1	no	—
60	C₂²×D₄	—	19	6	no	—
61	C₂²×D₄	—	19	4	no	—
62	#127	—	38	4	no	—
63	#126	—	38	4	no	—
64	C₂×C₄⋊C₄	—	19	3	no	—
65	C₂×C₂²⋊C₄	—	19	3	no	—
66	C₂×C₂²⋊C₄	—	19	12	no	—
67	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
68	#95	C₂×D₁₉	1	6	yes	—
69	C₁₉	#2818	1	1	yes	characteristic, complemented, Sylow
70	C₂⁴	—	19	1	no	—
71	C₂⁴	—	19	4	no	—
72	C₂×D₄	—	38	12	no	—
73	C₂×D₄	—	76	12	no	—
74	C₂×D₄	—	76	12	no	—
75	C₂²×C₄	—	19	3	no	—
76	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
77	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
78	C₄⋊C₄	—	38	6	no	—
79	C₂²⋊C₄	—	38	6	no	—
80	C₂²⋊C₄	—	76	12	no	—
81	C₄²	D₇₆	1	4	yes	complemented
82	C₂³	—	38	1	no	—
83	C₂³	—	38	4	no	—
84	C₂³	—	38	12	no	—
85	C₂³	—	38	12	no	—
86	C₂³	—	38	6	no	—
87	C₂³	C₂³×D₁₉	1	1	yes	characteristic
88	D₄	—	76	24	no	—
89	D₄	—	76	16	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	38	3	no	—
93	C₂×C₄	—	38	6	no	—
94	C₂×C₄	C₂×D₇₆	1	6	yes	—
95	C₂²	—	76	12	no	—
96	C₂²	—	76	3	no	—
97	C₂²	—	76	4	no	—
98	C₂²	—	76	4	no	—
99	C₂²	—	76	12	no	—
100	C₂²	C₂²×D₇₆	1	1	yes	characteristic
101	C₂²	#10597435	1	6	yes	—
102	C₄	—	2	6	no	—
103	C₄	—	4	4	no	—
104	C₄	—	76	3	no	—
105	C₂	—	152	4	no	—
106	C₂	—	152	1	no	—
107	C₂	#11927113	1	3	yes	—
108	C₂	#11927285	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597320

C₂

yes

maximal, characteristic, complemented

C₂×#10597322

C₂

yes

maximal, characteristic, complemented

#11926462

C₂

yes

maximal, complemented

#11926454

C₂

yes

maximal, complemented

C₁₉×#383

C₂

yes

maximal, characteristic, complemented

C₂²×D₇₆

C₂²

yes

—

C₂²×D₇₆

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×(C₂×D₁₉)⋊C₄

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

#10597322

—

#10597320

—

C₁₉×#95

C₂²

yes

—

C₂³×D₁₉

C₂³

yes

characteristic

C₂³×D₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄²×C₁₉

D₄

yes

complemented

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₂³×C₁₉

C₂⁴

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

#2818

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

H(5,𝔽₂)

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

#535

yes

—

C₂×C₁₉

#560

yes

—

D₁₉

—

D₁₉

—

C₂²×D₄

—

C₂²×D₄

—

#127

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#95

C₂×D₁₉

yes

—

C₁₉

#2818

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

D₇₆

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₁₉

yes

characteristic

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₇₆

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

C₂²×D₇₆

yes

characteristic

101

C₂²

#10597435

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₂

—

152

—

106

C₂

—

152

—

107

C₂

#11927113

yes

—

108

C₂

#11927285

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₁₉×#383	C₂
hypercenter	#383	D₁₉
hypocenter	C₁₉	#2818
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₁₉×#383

C₂

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
1. C₂×#10597320	C₂	semidirect
2. C₂×#10597322	C₂	semidirect
3. #11926462	C₂	semidirect
4. #11926454	C₂	semidirect
5. C₁₉×#383	C₂	semidirect
23. C₄²×C₁₉	D₄	semidirect
55. #383	D₁₉	semidirect
69. C₁₉	#2818	semidirect
81. C₄²	D₇₆	semidirect

H ≅ G/N

type

1. C₂×#10597320

C₂

semidirect

2. C₂×#10597322

C₂

semidirect

3. #11926462

C₂

semidirect

4. #11926454

C₂

semidirect

5. C₁₉×#383

C₂

semidirect

23. C₄²×C₁₉

D₄

semidirect

55. #383

D₁₉

semidirect

69. C₁₉

#2818

semidirect

81. C₄²

D₇₆

semidirect

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

subgroup	index
C₂×#10597320	2
C₂×#10597322	2
#11926462	2
#11926454	2
C₁₉×#383	2
#2818	19

subgroup

index

C₁₉×#383

Subgroups — #14571678

Conjugacy classes of subgroups

Complements

Maximal subgroups