Group #28588934 — subgroups

Subgroups — D₅₉×#1840 #28588934

Order 15104.

894 conjugacy classes of subgroups; only the 283 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 283 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	#376×D₅₉	C₂	1	1	yes	maximal, characteristic
2	#21424241	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424240	C₂	1	6	yes	maximal, complemented
4	#336×D₅₉	C₂	1	6	yes	maximal
5	C₅₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₅₉	C₂²	1	4	yes	—
7	C₂×C₄²×D₅₉	C₂²	1	3	yes	—
8	#16837248	C₂²	1	3	yes	—
9	#16837247	C₄	1	4	yes	—
10	#95×D₅₉	C₄	1	4	yes	—
11	#16837157	C₂²	1	6	yes	—
12	#16837156	C₂²	1	12	yes	—
13	C₅₉×#376	C₂²	1	1	yes	characteristic
14	C₅₉×#336	C₂²	1	6	yes	—
15	C₂²×C₄×D₅₉	C₂×C₄	1	6	yes	—
16	C₂²×C₄×D₅₉	C₂³	1	1	yes	characteristic
17	C₂²×C₅₉⋊C₈	C₂³	1	4	yes	—
18	C₂×C₈×D₅₉	—	2	24	no	—
19	C₂×C₄×Dic₅₉	C₂×C₄	1	6	yes	—
20	C₂×C₄×Dic₅₉	C₂³	1	3	yes	—
21	C₄²×D₅₉	—	2	12	no	—
22	C₅₉⋊#95	C₂×C₄	1	12	yes	—
23	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
24	C₂×C₄²×C₅₉	C₂³	1	3	yes	—
25	#95×C₅₉	C₂×C₄	1	4	yes	—
26	C₂³×D₅₉	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₅₉	C₂²×C₄	1	6	yes	—
28	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
29	C₂²×Dic₅₉	C₂²×C₄	1	6	yes	—
30	C₂²×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×D₅₉	—	2	12	no	—
32	C₂×C₄×D₅₉	—	2	24	no	—
33	C₂×C₄×D₅₉	#41	1	12	yes	—
34	C₂×C₈×C₅₉	—	2	12	no	—
35	C₄²×C₅₉	—	2	6	no	—
36	C₄×Dic₅₉	—	2	6	no	—
37	C₄×Dic₅₉	—	2	12	no	—
38	C₂×C₅₉⋊C₈	—	2	12	no	—
39	C₈×D₅₉	—	4	16	no	—
40	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
41	C₂²×D₅₉	#117	1	6	yes	—
42	C₂²×D₅₉	#131	1	8	yes	—
43	C₂×C₄×C₅₉	—	2	6	no	—
44	C₂×C₄×C₅₉	—	2	12	no	—
45	C₂×C₄×C₅₉	C₂×#41	1	6	yes	—
46	C₂×Dic₅₉	—	2	6	no	—
47	C₂×Dic₅₉	—	2	12	no	—
48	C₂×Dic₅₉	#117	1	6	yes	—
49	C₄×D₅₉	—	4	24	no	—
50	C₄×D₅₉	#126	1	16	yes	—
51	C₈×C₅₉	—	4	4	no	—
52	C₅₉⋊C₈	—	4	4	no	—
53	C₂×#1840	—	59	1	no	maximal, Sylow
54	C₂²×C₅₉	C₂×#117	1	3	yes	—
55	C₂²×C₅₉	C₂×#131	1	4	yes	—
56	C₂×D₅₉	#383	1	4	yes	—
57	C₂×D₅₉	#433	1	24	yes	—
58	C₄×C₅₉	—	4	6	no	—
59	C₄×C₅₉	C₂×#126	1	4	yes	—
60	Dic₅₉	—	4	6	no	—
61	Dic₅₉	#383	1	4	yes	—
62	C₂×#376	—	59	1	no	—
63	#1840	—	59	1	no	—
64	#1840	—	59	6	no	—
65	#1840	D₅₉	1	1	yes	characteristic, direct product factor
66	C₂×#336	—	59	6	no	—
67	C₂×C₅₉	C₂×#383	1	1	yes	characteristic
68	C₂×C₅₉	C₂×#433	1	6	yes	—
69	D₅₉	#1840	1	8	yes	direct product factor
70	C₂³×C₈	—	59	4	no	—
71	C₂²×C₄²	—	59	3	no	—
72	#376	—	59	3	no	—
73	#376	—	59	4	no	—
74	#376	C₂×D₅₉	1	1	yes	characteristic
75	C₂×#95	—	59	4	no	—
76	#336	—	59	12	no	—
77	#336	—	59	6	no	—
78	#336	C₂×D₅₉	1	6	yes	—
79	C₅₉	C₂×#1840	1	1	yes	characteristic, complemented, Sylow
80	C₂³×C₄	—	59	1	no	—
81	C₂³×C₄	—	59	6	no	—
82	C₂²×C₈	—	59	4	no	—
83	C₂²×C₈	—	118	24	no	—
84	C₂²×C₈	C₂²×D₅₉	1	4	yes	—
85	C₂×C₄²	—	59	6	no	—
86	C₂×C₄²	—	59	3	no	—
87	C₂×C₄²	—	118	12	no	—
88	C₂×C₄²	C₂²×D₅₉	1	3	yes	—
89	#95	—	59	12	no	—
90	#95	C₄×D₅₉	1	4	yes	—
91	C₂⁴	—	59	1	no	—
92	C₂²×C₄	—	59	1	no	—
93	C₂²×C₄	—	59	12	no	—
94	C₂²×C₄	—	59	6	no	—
95	C₂²×C₄	—	118	12	no	—
96	C₂²×C₄	—	118	24	no	—
97	C₂²×C₄	C₂×C₄×D₅₉	1	6	yes	—
98	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
99	C₂×C₈	—	2	12	no	—
100	C₂×C₈	—	118	12	no	—
101	C₂×C₈	—	236	16	no	—
102	C₄²	—	2	6	no	—
103	C₄²	—	118	12	no	—
104	C₄²	—	118	6	no	—
105	C₂³	—	59	8	no	—
106	C₂³	—	59	6	no	—
107	C₂³	C₂²×C₄×D₅₉	1	1	yes	characteristic
108	C₂×C₄	—	2	12	no	—
109	C₂×C₄	—	2	6	no	—
110	C₂×C₄	—	59	6	no	—
111	C₂×C₄	—	59	16	no	—
112	C₂×C₄	—	118	12	no	—
113	C₂×C₄	—	118	6	no	—
114	C₂×C₄	—	236	24	no	—
115	C₂×C₄	#41×D₅₉	1	6	yes	—
116	C₈	—	4	4	no	—
117	C₈	—	236	4	no	—
118	C₂²	—	59	4	no	—
119	C₂²	—	59	24	no	—
120	C₂²	#117×D₅₉	1	3	yes	—
121	C₂²	#131×D₅₉	1	4	yes	—
122	C₄	—	4	6	no	—
123	C₄	—	59	4	no	—
124	C₄	—	236	6	no	—
125	C₄	#126×D₅₉	1	4	yes	—
126	C₂	—	59	8	no	—
127	C₂	#383×D₅₉	1	1	yes	characteristic
128	C₂	#433×D₅₉	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#376×D₅₉

C₂

yes

maximal, characteristic

#21424241

C₂

yes

maximal, characteristic, complemented

#21424240

C₂

yes

maximal, complemented

#336×D₅₉

C₂

yes

maximal

C₅₉×#1840

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₅₉

C₂²

yes

—

C₂×C₄²×D₅₉

C₂²

yes

—

#16837248

C₂²

yes

—

#16837247

C₄

yes

—

#95×D₅₉

C₄

yes

—

#16837157

C₂²

yes

—

#16837156

C₂²

yes

—

C₅₉×#376

C₂²

yes

characteristic

C₅₉×#336

C₂²

yes

—

C₂²×C₄×D₅₉

C₂×C₄

yes

—

C₂²×C₄×D₅₉

C₂³

yes

characteristic

C₂²×C₅₉⋊C₈

C₂³

yes

—

C₂×C₈×D₅₉

—

C₂×C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₄×Dic₅₉

C₂³

yes

—

C₄²×D₅₉

—

C₅₉⋊#95

C₂×C₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

—

C₂×C₄²×C₅₉

C₂³

yes

—

#95×C₅₉

C₂×C₄

yes

—

C₂³×D₅₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂²×C₄

yes

—

C₂²×C₄×C₅₉

C₂⁴

yes

characteristic

C₂²×Dic₅₉

C₂²×C₄

yes

—

C₂²×Dic₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

#41

yes

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₈×D₅₉

—

C₂³×C₅₉

C₂³×C₄

yes

characteristic

C₂²×D₅₉

#117

yes

—

C₂²×D₅₉

#131

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×#41

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

#117

yes

—

C₄×D₅₉

—

C₄×D₅₉

#126

yes

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂×#1840

—

maximal, Sylow

C₂²×C₅₉

C₂×#117

yes

—

C₂²×C₅₉

C₂×#131

yes

—

C₂×D₅₉

#383

yes

—

C₂×D₅₉

#433

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂×#126

yes

—

Dic₅₉

—

Dic₅₉

#383

yes

—

—

—

—

D₅₉

yes

characteristic, direct product factor

C₂×#336

—

C₂×C₅₉

C₂×#383

yes

characteristic

C₂×C₅₉

C₂×#433

yes

—

D₅₉

#1840

yes

direct product factor

C₂³×C₈

—

C₂²×C₄²

—

#376

—

#376

—

#376

C₂×D₅₉

yes

characteristic

C₂×#95

—

#336

—

#336

—

#336

C₂×D₅₉

yes

—

C₅₉

C₂×#1840

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

118

—

C₂²×C₈

C₂²×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

118

—

C₂×C₄²

C₂²×D₅₉

yes

—

#95

—

#95

C₄×D₅₉

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

C₂×C₄×D₅₉

yes

—

C₂²×C₄

C₂³×D₅₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

118

—

101

C₂×C₈

—

236

—

102

C₄²

—

103

C₄²

—

118

—

104

C₄²

—

118

—

105

C₂³

—

106

C₂³

—

107

C₂³

C₂²×C₄×D₅₉

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

118

—

113

C₂×C₄

—

118

—

114

C₂×C₄

—

236

—

115

C₂×C₄

#41×D₅₉

yes

—

116

C₈

—

117

C₈

—

236

—

118

C₂²

—

119

C₂²

—

120

C₂²

#117×D₅₉

yes

—

121

C₂²

#131×D₅₉

yes

—

122

C₄

—

123

C₄

—

124

C₄

—

236

—

125

C₄

#126×D₅₉

yes

—

126

C₂

—

127

C₂

#383×D₅₉

yes

characteristic

128

C₂

#433×D₅₉

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂³×C₄
Fitting	C₅₉×#1840	C₂
prime radical	C₂³×D₅₉	C₂²×C₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1840	D₅₉
hypocenter	C₅₉	C₂×#1840
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1840

subgroup

G/H

center, Frattini

C₂²×C₄

C₂³×D₅₉

commutator, socle

C₂³×C₅₉

C₂³×C₄

Fitting

C₅₉×#1840

C₂

prime radical

C₂³×D₅₉

C₂²×C₄

cosocle

C₂²×C₄×C₅₉

C₂⁴

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂²×C₄ ◁ #1840

N	H ≅ G/N	type
2. #21424241	C₂	semidirect
3. #21424240	C₂	semidirect
5. C₅₉×#1840	C₂	semidirect
65. #1840	D₅₉	direct (N × H)
69. D₅₉	#1840	direct (N × H)
79. C₅₉	C₂×#1840	semidirect

H ≅ G/N

type

2. #21424241

C₂

semidirect

3. #21424240

C₂

semidirect

5. C₅₉×#1840

C₂

semidirect

65. #1840

D₅₉

direct (N × H)

69. D₅₉

#1840

direct (N × H)

79. C₅₉

C₂×#1840

semidirect

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

subgroup	index
#376×D₅₉	2
#21424241	2
#21424240	2
#336×D₅₉	2
C₅₉×#1840	2
C₂×#1840	59

subgroup

index

#376×D₅₉

#21424241

#21424240

#336×D₅₉

C₅₉×#1840

C₂×#1840

Subgroups — D₅₉×#1840 #28588934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D59×#1840 #28588934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×#1840 #28588934