Group #15756577 — subgroups

Subgroups — #15756577

Order 3328.

262 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 115 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	#13113584	C₂	1	2	yes	maximal
2	#13112681	C₂	1	2	yes	maximal
3	#13112665	C₂	1	2	yes	maximal
4	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#376	C₂²	1	1	yes	characteristic
8	#11718586	C₂²	1	4	yes	—
9	C₁₃×#336	C₄	1	4	yes	—
10	#11718050	—	2	2	no	—
11	#11718049	—	2	2	no	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×#97	—	2	2	no	—
17	C₄×C₈×C₁₃	D₄	1	2	yes	—
18	C₄×C₈×C₁₃	Q₈	1	2	yes	—
19	C₁₃×#95	—	2	2	no	—
20	C₂²⋊#1055	—	2	4	no	—
21	C₄⋊#1055	—	2	4	no	—
22	C₄×#1055	—	2	4	no	—
23	#8783	—	13	1	no	maximal, Sylow
24	C₂²×C₄×C₁₃	—	2	2	no	—
25	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₃	#41	1	2	yes	—
27	C₂×C₈×C₁₃	—	2	4	no	—
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	—	2	4	no	—
30	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
31	C₄²×C₁₃	—	2	4	no	—
32	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₄²×C₁₃	#41	1	2	yes	—
35	C₂×#1055	—	4	4	no	—
36	#1746	D₁₃	1	1	yes	characteristic
37	#1564	—	13	2	no	—
38	#1281	—	13	2	no	—
39	#1274	—	13	2	no	—
40	C₂³×C₁₃	#117	1	1	yes	characteristic
41	C₂×C₄×C₁₃	—	4	2	no	—
42	C₂×C₄×C₁₃	—	4	4	no	—
43	C₂×C₄×C₁₃	—	4	2	no	—
44	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
46	C₂×C₄×C₁₃	#124	1	2	yes	—
47	C₂×C₄×C₁₃	#125	1	2	yes	—
48	C₂×C₄×C₁₃	#131	1	4	yes	—
49	C₈×C₁₃	—	2	4	no	—
50	C₈×C₁₃	—	4	2	no	—
51	#1055	—	8	4	no	—
52	#431	—	13	4	no	—
53	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
54	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
55	#376	C₂×D₁₃	1	1	yes	characteristic
56	#336	Dic₁₃	1	4	yes	—
57	#335	—	26	2	no	—
58	#334	—	26	2	no	—
59	C₂²×C₁₃	—	2	2	no	—
60	C₂²×C₁₃	#382	1	1	yes	characteristic
61	C₂²×C₁₃	#433	1	2	yes	—
62	C₄×C₁₃	—	2	2	no	—
63	C₄×C₁₃	—	2	2	no	—
64	C₄×C₁₃	—	8	2	no	—
65	C₄×C₁₃	#424	1	2	yes	—
66	C₄×C₁₃	#433	1	2	yes	—
67	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
68	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
69	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
70	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
71	C₄⋊C₈	—	26	4	no	—
72	C₂²⋊C₈	—	26	4	no	—
73	#97	—	2	2	no	—
74	C₄×C₈	—	26	4	no	—
75	C₄×C₈	Dic₂₆	1	2	yes	—
76	C₄×C₈	D₅₂	1	2	yes	—
77	#95	—	2	2	no	—
78	C₂×C₁₃	—	2	2	no	—
79	C₂×C₁₃	#1832	1	1	yes	characteristic
80	C₂×C₁₃	#1833	1	2	yes	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	#6127	1	2	yes	—
83	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
84	C₂×C₈	—	2	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	2	4	no	—
87	C₂×C₈	—	52	4	no	—
88	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
89	C₄²	—	2	4	no	—
90	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
91	C₄²	C₂×D₅₂	1	1	yes	characteristic
92	C₄²	#6127	1	2	yes	—
93	C₁₃	#8783	1	1	yes	characteristic, complemented, Sylow
94	C₂³	#88180	1	1	yes	characteristic
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	4	4	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	#88124	1	2	yes	—
99	C₂×C₄	#88129	1	2	yes	—
100	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
101	C₂×C₄	#88180	1	1	yes	characteristic
102	C₂×C₄	#88202	1	4	yes	—
103	C₈	—	2	4	no	—
104	C₈	—	4	2	no	—
105	C₈	—	104	4	no	—
106	C₂²	—	2	2	no	—
107	C₂²	#11718597	1	1	yes	characteristic
108	C₂²	#11718661	1	2	yes	—
109	C₄	—	2	2	no	—
110	C₄	—	2	2	no	—
111	C₄	—	8	2	no	—
112	C₄	#11718660	1	2	yes	—
113	C₄	#11718661	1	2	yes	—
114	C₂	—	2	2	no	—
115	C₂	#13114956	1	1	yes	characteristic
116	C₂	#13114960	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13113584

C₂

yes

maximal

#13112681

C₂

yes

maximal

#13112665

C₂

yes

maximal

C₁₃×#1746

C₂

yes

maximal, characteristic

C₂×C₁₃×#97

C₂²

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#376

C₂²

yes

characteristic

#11718586

C₂²

yes

—

C₁₃×#336

C₄

yes

—

#11718050

—

#11718049

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#97

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₁₃×#95

—

C₂²⋊#1055

—

—

—

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

#41

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

characteristic

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₂×#1055

—

#1746

D₁₃

yes

—

—

—

C₂³×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#125

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#431

—

C₂×#97

C₂×D₁₃

yes

characteristic

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

#376

C₂×D₁₃

yes

characteristic

#336

Dic₁₃

yes

—

#335

—

#334

—

C₂²×C₁₃

—

C₂²×C₁₃

#382

yes

characteristic

C₂²×C₁₃

#433

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#424

yes

—

C₄×C₁₃

#433

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

Dic₂₆

yes

—

C₄×C₈

D₅₂

yes

—

#95

—

C₂×C₁₃

—

C₂×C₁₃

#1832

yes

characteristic

C₂×C₁₃

#1833

yes

—

C₂²×C₄

—

C₂²×C₄

#6127

yes

—

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄⋊Dic₁₃

yes

—

C₄²

—

C₄²

C₂×Dic₂₆

yes

characteristic

C₄²

C₂×D₅₂

yes

characteristic

C₄²

#6127

yes

—

C₁₃

#8783

yes

characteristic, complemented, Sylow

C₂³

#88180

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#88124

yes

—

C₂×C₄

#88129

yes

—

100

C₂×C₄

C₂×C₄⋊Dic₁₃

yes

characteristic

101

C₂×C₄

#88180

yes

characteristic

102

C₂×C₄

#88202

yes

—

103

C₈

—

104

C₈

—

105

C₈

—

104

—

106

C₂²

—

107

C₂²

#11718597

yes

characteristic

108

C₂²

#11718661

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

#11718660

yes

—

113

C₄

#11718661

yes

—

114

C₂

—

115

C₂

#13114956

yes

characteristic

116

C₂

#13114960

yes

—

	subgroup	G/H
center	C₂×C₄	#88180
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1746	C₂
socle	C₂²×C₁₃	#382
prime radical	C₂³×C₁₃	#117
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1746	D₁₃
hypocenter	C₁₃	#8783
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

subgroup

G/H

center

C₂×C₄

#88180

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1746

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ #376 ◁ #1746

N	H ≅ G/N	type
93. C₁₃	#8783	semidirect

H ≅ G/N

type

93. C₁₃

#8783

semidirect

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

subgroup	index
#13113584	2
#13112681	2
#13112665	2
C₁₃×#1746	2
#8783	13

subgroup

index

C₁₃×#1746

Subgroups — #15756577

Conjugacy classes of subgroups

Complements

Maximal subgroups