Group #14577783 — subgroups

Subgroups — #14577783

Order 2432.

930 conjugacy classes of subgroups; only the 451 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 451 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	#11927298	C₂	1	10	yes	maximal, complemented
2	#11927292	C₂	1	5	yes	maximal, complemented
3	#11927100	C₂	1	5	yes	maximal, complemented
4	#11927079	C₂	1	10	yes	maximal, complemented
5	C₁₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#125	C₂²	1	10	yes	—
7	C₁₉×#125	C₂²	1	5	yes	—
8	#10597344	C₂²	1	20	yes	—
9	#10597343	C₂²	1	10	yes	—
10	#10597342	C₂²	1	20	yes	—
11	#10597341	C₂²	1	10	yes	—
12	#10597340	C₂²	1	20	yes	—
13	#10597339	C₂²	1	10	yes	—
14	#10597338	C₂²	1	10	yes	—
15	#10597334	C₂²	1	10	yes	—
16	#10597333	C₂²	1	10	yes	—
17	#10597321	C₂²	1	10	yes	—
18	C₄²×D₁₉	C₂²	1	5	yes	—
19	#10597316	C₂²	1	5	yes	—
20	C₂×D₇₆	C₂³	1	10	yes	—
21	C₂×C₄×D₁₉	C₂³	1	5	yes	—
22	C₂×C₄×D₁₉	C₂³	1	10	yes	—
23	C₂×Dic₃₈	C₂³	1	10	yes	—
24	C₄⋊C₄×C₁₉	C₂³	1	10	yes	—
25	C₄⋊C₄×C₁₉	C₂³	1	10	yes	—
26	C₄⋊C₄×C₁₉	C₂³	1	10	yes	—
27	C₄²×C₁₉	C₂³	1	5	yes	—
28	(C₂×D₁₉)⋊C₄	C₂³	1	20	yes	—
29	(C₂×D₁₉)⋊C₄	C₂³	1	20	yes	—
30	C₄⋊Dic₁₉	C₂³	1	10	yes	—
31	Dic₁₉⋊C₄	C₂³	1	20	yes	—
32	C₄×Dic₁₉	C₂³	1	10	yes	—
33	C₄×Dic₁₉	C₂³	1	5	yes	—
34	C₂²×D₁₉	C₂⁴	1	5	yes	—
35	C₂×C₄×C₁₉	C₂⁴	1	10	yes	—
36	C₂×C₄×C₁₉	C₂⁴	1	5	yes	—
37	C₂×Dic₁₉	C₂⁴	1	10	yes	—
38	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
39	D₇₆	—	4	10	no	—
40	C₄×D₁₉	—	2	10	no	—
41	C₄×D₁₉	—	4	10	no	—
42	Dic₃₈	—	4	10	no	—
43	#3531	—	19	1	no	maximal, Sylow
44	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
45	C₂×D₁₉	—	2	5	no	—
46	C₂×D₁₉	—	2	10	no	—
47	C₄×C₁₉	—	2	5	no	—
48	C₄×C₁₉	—	2	10	no	—
49	Dic₁₉	—	2	10	no	—
50	Dic₁₉	2₋¹⁺⁴	1	2	yes	—
51	#564	D₁₉	1	1	yes	characteristic, complemented
52	#563	—	19	10	no	—
53	#562	—	19	5	no	—
54	#533	—	19	5	no	—
55	#529	—	19	10	no	—
56	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
57	C₂×C₁₉	#585	1	2	yes	—
58	D₁₉	—	4	5	no	—
59	C₄⋊Q₈	—	19	10	no	—
60	#126	—	19	20	no	—
61	#125	—	19	5	no	—
62	#125	C₂×D₁₉	1	10	yes	—
63	#125	C₂×D₁₉	1	5	yes	—
64	#124	—	19	10	no	—
65	#123	—	19	20	no	—
66	C₂²⋊Q₈	—	19	10	no	—
67	C₂²⋊Q₈	—	19	20	no	—
68	#121	—	19	10	no	—
69	C₄×Q₈	—	19	10	no	—
70	C₄×D₄	—	19	10	no	—
71	#117	—	19	10	no	—
72	C₂×C₄²	—	19	5	no	—
73	C₁₉	#3531	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	19	10	no	—
75	C₂×D₄	—	19	10	no	—
76	C₂²×C₄	—	19	5	no	—
77	C₂²×C₄	—	19	10	no	—
78	C₄⋊C₄	—	19	20	no	—
79	C₄⋊C₄	—	19	10	no	—
80	C₄⋊C₄	C₂²×D₁₉	1	10	yes	—
81	C₄⋊C₄	C₂²×D₁₉	1	10	yes	—
82	C₄⋊C₄	C₂²×D₁₉	1	10	yes	—
83	C₂²⋊C₄	—	19	20	no	—
84	C₂²⋊C₄	—	19	20	no	—
85	C₄²	—	19	10	no	—
86	C₄²	—	19	5	no	—
87	C₄²	C₂²×D₁₉	1	5	yes	—
88	C₂³	—	19	5	no	—
89	Q₈	—	76	10	no	—
90	D₄	—	76	10	no	—
91	C₂×C₄	—	19	1	no	—
92	C₂×C₄	—	19	10	no	—
93	C₂×C₄	—	38	10	no	—
94	C₂×C₄	—	76	10	no	—
95	C₂×C₄	C₂³×D₁₉	1	5	yes	—
96	C₂×C₄	C₂³×D₁₉	1	10	yes	—
97	C₂²	—	38	5	no	—
98	C₂²	—	38	10	no	—
99	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
100	C₄	—	2	5	no	—
101	C₄	—	2	10	no	—
102	C₄	—	19	2	no	—
103	C₄	—	38	10	no	—
104	C₂	—	76	5	no	—
105	C₂	2₋¹⁺⁴×D₁₉	1	1	yes	characteristic
106	C₂	#11927381	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927298

C₂

yes

maximal, complemented

#11927292

C₂

yes

maximal, complemented

#11927100

C₂

yes

maximal, complemented

#11927079

C₂

yes

maximal, complemented

C₁₉×#564

C₂

yes

maximal, characteristic, complemented

C₁₉×#125

C₂²

yes

—

C₁₉×#125

C₂²

yes

—

#10597344

C₂²

yes

—

#10597343

C₂²

yes

—

#10597342

C₂²

yes

—

#10597341

C₂²

yes

—

#10597340

C₂²

yes

—

#10597339

C₂²

yes

—

#10597338

C₂²

yes

—

#10597334

C₂²

yes

—

#10597333

C₂²

yes

—

#10597321

C₂²

yes

—

C₄²×D₁₉

C₂²

yes

—

#10597316

C₂²

yes

—

C₂×D₇₆

C₂³

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×C₄×D₁₉

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₄²×C₁₉

C₂³

yes

—

(C₂×D₁₉)⋊C₄

C₂³

yes

—

(C₂×D₁₉)⋊C₄

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂²×D₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

characteristic

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

#3531

—

maximal, Sylow

C₂²×C₁₉

C₂⁵

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

2₋¹⁺⁴

yes

—

#564

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

C₂×2₋¹⁺⁴

yes

characteristic

C₂×C₁₉

#585

yes

—

D₁₉

—

C₄⋊Q₈

—

#126

—

#125

—

#125

C₂×D₁₉

yes

—

#125

C₂×D₁₉

yes

—

#124

—

#123

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

#121

—

C₄×Q₈

—

C₄×D₄

—

#117

—

C₂×C₄²

—

C₁₉

#3531

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₉

yes

—

C₂³

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂³×D₁₉

yes

—

C₂×C₄

C₂³×D₁₉

yes

—

C₂²

—

C₂²

—

C₂²

C₂⁴×D₁₉

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₂

—

105

C₂

2₋¹⁺⁴×D₁₉

yes

characteristic

106

C₂

#11927381

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#564	C₂
hypercenter	#564	D₁₉
hypocenter	C₁₉	#3531
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #564

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₉

commutator, socle, cosocle

C₂²×C₁₉

C₂⁵

Fitting

C₁₉×#564

C₂

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ #564

N	H ≅ G/N	type
1. #11927298	C₂	semidirect
2. #11927292	C₂	semidirect
3. #11927100	C₂	semidirect
4. #11927079	C₂	semidirect
5. C₁₉×#564	C₂	semidirect
51. #564	D₁₉	semidirect
73. C₁₉	#3531	semidirect

H ≅ G/N

type

1. #11927298

C₂

semidirect

2. #11927292

C₂

semidirect

3. #11927100

C₂

semidirect

4. #11927079

C₂

semidirect

5. C₁₉×#564

C₂

semidirect

51. #564

D₁₉

semidirect

73. C₁₉

#3531

semidirect

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

subgroup	index
#11927298	2
#11927292	2
#11927100	2
#11927079	2
C₁₉×#564	2
#3531	19

subgroup

index

C₁₉×#564

Subgroups — #14577783

Conjugacy classes of subgroups

Complements

Maximal subgroups