Group #28319361 — subgroups

Subgroups — D₅₃⋊#1840 #28319361

Order 13568.

894 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 272 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	#20290644	C₂	1	8	yes	maximal, complemented
2	#20290376	C₂	1	6	yes	maximal
3	#376×D₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₅₃⋊C₈	C₂²	1	4	yes	—
5	#16811489	C₂²	1	24	yes	—
6	C₂×C₄²×D₅₃	C₂²	1	3	yes	—
7	#16810469	C₄	1	3	yes	—
8	#16810468	C₂²	1	4	yes	—
9	#95×D₅₃	C₄	1	4	yes	—
10	C₅₃×#376	C₄	1	1	yes	characteristic
11	C₂×D₅₃⋊C₈	—	2	24	no	—
12	C₂²×#88324	C₂³	1	8	yes	—
13	C₂²×C₄×D₅₃	C₂×C₄	1	6	yes	—
14	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×Dic₅₃	C₂×C₄	1	3	yes	—
16	C₂×C₄×Dic₅₃	C₂³	1	6	yes	—
17	C₄²×D₅₃	—	2	12	no	—
18	#13133124	C₂×C₄	1	12	yes	—
19	C₂×C₄²×C₅₃	C₂×C₄	1	3	yes	—
20	#95×C₅₃	C₂×C₄	1	4	yes	—
21	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₅₃	C₂²×C₄	1	6	yes	—
23	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×Dic₅₃	C₂²×C₄	1	6	yes	—
25	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
26	C₂×C₄×D₅₃	—	2	12	no	—
27	C₂×C₄×D₅₃	—	2	24	no	—
28	C₂×C₄×D₅₃	#41	1	12	yes	—
29	C₂×#88324	—	2	24	no	—
30	D₅₃⋊C₈	—	4	16	no	—
31	C₄²×C₅₃	—	2	6	no	—
32	C₄×Dic₅₃	—	2	6	no	—
33	C₄×Dic₅₃	—	2	12	no	—
34	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
35	C₂²×D₅₃	#117	1	6	yes	—
36	C₂²×D₅₃	#131	1	8	yes	—
37	C₂×C₄×C₅₃	—	2	6	no	—
38	C₂×C₄×C₅₃	—	2	12	no	—
39	C₂×C₄×C₅₃	#117	1	6	yes	—
40	C₂×Dic₅₃	—	2	6	no	—
41	C₂×Dic₅₃	—	2	12	no	—
42	C₂×Dic₅₃	C₂×#41	1	6	yes	—
43	C₄×D₅₃	—	4	24	no	—
44	C₄×D₅₃	#126	1	16	yes	—
45	#88324	—	4	8	no	—
46	C₂×#1840	—	53	1	no	maximal, Sylow
47	C₂²×C₅₃	C₂×#117	1	3	yes	—
48	C₂²×C₅₃	C₂×#131	1	4	yes	—
49	C₂×D₅₃	#383	1	4	yes	—
50	C₂×D₅₃	#433	1	24	yes	—
51	C₄×C₅₃	—	4	6	no	—
52	C₄×C₅₃	#383	1	4	yes	—
53	Dic₅₃	—	4	6	no	—
54	Dic₅₃	C₂×#126	1	4	yes	—
55	C₂×#376	—	53	1	no	—
56	#1840	—	53	8	no	—
57	C₂×#336	—	53	6	no	—
58	C₂×C₅₃	C₂×#383	1	1	yes	characteristic
59	C₂×C₅₃	C₂×#433	1	6	yes	—
60	D₅₃	#1840	1	8	yes	complemented
61	C₂³×C₈	—	53	4	no	—
62	C₂²×C₄²	—	53	3	no	—
63	#376	—	53	3	no	—
64	#376	—	53	4	no	—
65	#376	#6157	1	1	yes	characteristic
66	C₂×#95	—	53	4	no	—
67	#336	—	53	24	no	—
68	C₅₃	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
69	C₂³×C₄	—	53	1	no	—
70	C₂³×C₄	—	53	6	no	—
71	C₂²×C₈	—	53	8	no	—
72	C₂²×C₈	—	106	24	no	—
73	C₂×C₄²	—	53	6	no	—
74	C₂×C₄²	—	53	3	no	—
75	C₂×C₄²	—	106	12	no	—
76	C₂×C₄²	C₂×#6157	1	3	yes	—
77	#95	—	53	12	no	—
78	#95	C₂×#6157	1	4	yes	—
79	C₂⁴	—	53	1	no	—
80	C₂²×C₄	—	53	1	no	—
81	C₂²×C₄	—	53	12	no	—
82	C₂²×C₄	—	53	6	no	—
83	C₂²×C₄	—	106	12	no	—
84	C₂²×C₄	—	106	24	no	—
85	C₂²×C₄	C₂²×#6157	1	6	yes	—
86	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
87	C₂×C₈	—	106	24	no	—
88	C₂×C₈	—	212	16	no	—
89	C₄²	—	2	6	no	—
90	C₄²	—	106	12	no	—
91	C₄²	—	106	6	no	—
92	C₂³	—	53	6	no	—
93	C₂³	—	53	8	no	—
94	C₂³	C₂³×#6157	1	1	yes	characteristic
95	C₂×C₄	—	2	6	no	—
96	C₂×C₄	—	2	12	no	—
97	C₂×C₄	—	53	6	no	—
98	C₂×C₄	—	53	16	no	—
99	C₂×C₄	—	106	6	no	—
100	C₂×C₄	—	106	12	no	—
101	C₂×C₄	—	212	24	no	—
102	C₂×C₄	#13133296	1	6	yes	—
103	C₈	—	212	8	no	—
104	C₂²	—	53	24	no	—
105	C₂²	—	53	4	no	—
106	C₂²	C₂×#13133296	1	3	yes	—
107	C₂²	D₅₃⋊#131	1	4	yes	—
108	C₄	—	4	6	no	—
109	C₄	—	53	4	no	—
110	C₄	—	212	6	no	—
111	C₄	#16811568	1	4	yes	—
112	C₂	—	53	8	no	—
113	C₂	C₂×#16811568	1	1	yes	characteristic
114	C₂	D₅₃⋊#433	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#20290644

C₂

yes

maximal, complemented

#20290376

C₂

yes

maximal

#376×D₅₃

C₂

yes

maximal, characteristic

C₂²×D₅₃⋊C₈

C₂²

yes

—

#16811489

C₂²

yes

—

C₂×C₄²×D₅₃

C₂²

yes

—

#16810469

C₄

yes

—

#16810468

C₂²

yes

—

#95×D₅₃

C₄

yes

—

C₅₃×#376

C₄

yes

characteristic

C₂×D₅₃⋊C₈

—

C₂²×#88324

C₂³

yes

—

C₂²×C₄×D₅₃

C₂×C₄

yes

—

C₂²×C₄×D₅₃

C₂³

yes

characteristic

C₂×C₄×Dic₅₃

C₂×C₄

yes

—

C₂×C₄×Dic₅₃

C₂³

yes

—

C₄²×D₅₃

—

#13133124

C₂×C₄

yes

—

C₂×C₄²×C₅₃

C₂×C₄

yes

—

#95×C₅₃

C₂×C₄

yes

—

C₂³×D₅₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂²×C₄

yes

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×Dic₅₃

C₂²×C₄

yes

—

C₂²×Dic₅₃

C₂⁴

yes

characteristic

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

—

C₂×C₄×D₅₃

#41

yes

—

C₂×#88324

—

D₅₃⋊C₈

—

C₄²×C₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₂³×C₅₃

C₂³×C₄

yes

characteristic

C₂²×D₅₃

#117

yes

—

C₂²×D₅₃

#131

yes

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#117

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×#41

yes

—

C₄×D₅₃

—

C₄×D₅₃

#126

yes

—

—

—

C₂²×C₅₃

yes

—

C₂²×C₅₃

C₂×#131

yes

—

C₂×D₅₃

#383

yes

—

C₂×D₅₃

#433

yes

—

C₄×C₅₃

—

C₄×C₅₃

#383

yes

—

Dic₅₃

—

Dic₅₃

C₂×#126

yes

—

C₂×#376

—

#1840

—

C₂×#336

—

C₂×C₅₃

C₂×#383

yes

characteristic

C₂×C₅₃

C₂×#433

yes

—

D₅₃

#1840

yes

complemented

C₂³×C₈

—

C₂²×C₄²

—

—

—

yes

C₂×#95

—

#336

—

C₅₃

C₂×#1840

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

106

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

106

—

C₂×C₄²

C₂×#6157

yes

—

#95

—

#95

C₂×#6157

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

106

—

C₂²×C₄

—

106

—

C₂²×C₄

C₂²×#6157

yes

—

C₂²×C₄

C₂²×#6157

yes

characteristic

C₂×C₈

—

106

—

C₂×C₈

—

212

—

C₄²

—

C₄²

—

106

—

C₄²

—

106

—

C₂³

—

C₂³

—

C₂³

C₂³×#6157

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

106

—

100

C₂×C₄

—

106

—

101

C₂×C₄

—

212

—

102

C₂×C₄

#13133296

yes

—

103

C₈

—

212

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×#13133296

yes

—

107

C₂²

D₅₃⋊#131

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

212

—

111

C₄

#16811568

yes

—

112

C₂

—

113

C₂

C₂×#16811568

yes

characteristic

114

C₂

D₅₃⋊#433

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×#6157
commutator, socle	C₂³×C₅₃	C₂³×C₄
Frattini	C₂³	C₂³×#6157
Fitting	C₅₃×#376	C₄
prime radical	C₂³×D₅₃	C₂²×C₄
cosocle	C₂²×Dic₅₃	C₂⁴
hypercenter	#376	#6157
hypocenter	C₅₃	C₂×#1840
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×#6157

commutator, socle

C₂³×C₅₃

C₂³×C₄

Frattini

C₂³

C₂³×#6157

Fitting

C₅₃×#376

C₄

prime radical

C₂³×D₅₃

C₂²×C₄

cosocle

C₂²×Dic₅₃

C₂⁴

C₅₃

G ▷ C₂³×C₅₃ ▷ C₅₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
1. #20290644	C₂	semidirect
60. D₅₃	#1840	semidirect
68. C₅₃	C₂×#1840	semidirect

H ≅ G/N

type

1. #20290644

C₂

semidirect

60. D₅₃

#1840

semidirect

68. C₅₃

C₂×#1840

semidirect

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

subgroup	index
#20290644	2
#20290376	2
#376×D₅₃	2
C₂×#1840	53

subgroup

index

#20290644

#20290376

#376×D₅₃

C₂×#1840

Subgroups — D₅₃⋊#1840 #28319361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D53⋊#1840 #28319361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#1840 #28319361