Group #15765685 — subgroups

Subgroups — #15765685

Order 3328.

478 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 89 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	#13126230	C₂	1	3	yes	maximal
2	#13115812	C₂	1	3	yes	maximal
3	C₁₃×#1309	C₂	1	1	yes	maximal, characteristic
4	#11719175	C₂²	1	3	yes	—
5	C₁₃×#423	C₂²	1	3	yes	—
6	#11718798	—	2	6	no	—
7	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
8	#11718512	—	2	6	no	—
9	#11718510	—	2	6	no	—
10	#11718147	—	2	6	no	—
11	C₂×C₁₃×M₁₆	D₄	1	6	yes	—
12	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
13	#88180	—	2	3	no	—
14	#88178	—	2	6	no	—
15	C₂×C₄×Dic₁₃	—	2	3	no	—
16	C₂×Dic₅₂	—	2	6	no	—
17	#88124	—	2	3	no	—
18	#88123	D₄	1	6	yes	—
19	C₄×Dic₂₆	—	2	6	no	—
20	C₁₃×C₄⋊C₈	—	2	6	no	—
21	#88057	—	2	6	no	—
22	#88056	—	2	12	no	—
23	#10303	—	13	1	no	maximal, Sylow
24	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
25	C₂²×Dic₁₃	—	4	1	no	—
26	C₂×Dic₂₆	—	2	6	no	—
27	C₁₃×M₁₆	—	4	6	no	—
28	C₂×C₈×C₁₃	—	2	6	no	—
29	C₄²×C₁₃	C₂×D₄	1	3	yes	—
30	C₄²×C₁₃	#41	1	1	yes	characteristic
31	C₂²⋊Dic₁₃	—	4	3	no	—
32	C₄⋊Dic₁₃	—	2	6	no	—
33	C₄⋊Dic₁₃	—	2	6	no	—
34	#6101	—	4	6	no	—
35	C₄×Dic₁₃	—	2	6	no	—
36	C₄×Dic₁₃	—	4	3	no	—
37	C₄×Dic₁₃	—	4	3	no	—
38	Dic₅₂	—	8	6	no	—
39	#3255	—	13	3	no	—
40	#1994	—	13	3	no	—
41	#1309	D₁₃	1	1	yes	characteristic
42	C₂³×C₁₃	#127	1	1	yes	characteristic
43	C₂×C₄×C₁₃	—	2	3	no	—
44	C₂×C₄×C₁₃	—	2	3	no	—
45	C₂×C₄×C₁₃	#120	1	3	yes	—
46	C₂×C₄×C₁₃	#121	1	3	yes	—
47	C₂×Dic₁₃	—	4	6	no	—
48	C₂×Dic₁₃	—	4	6	no	—
49	Dic₂₆	—	4	6	no	—
50	Dic₂₆	—	4	6	no	—
51	C₈×C₁₃	—	4	6	no	—
52	#533	—	13	3	no	—
53	#475	—	26	6	no	—
54	#470	—	26	6	no	—
55	#462	—	26	6	no	—
56	#423	C₂×D₁₃	1	3	yes	—
57	C₄³	—	13	1	no	—
58	#339	—	26	6	no	—
59	C₂²×C₁₃	—	2	3	no	—
60	C₂²×C₁₃	#392	1	1	yes	characteristic
61	C₄×C₁₃	—	2	3	no	—
62	C₄×C₁₃	#455	1	3	yes	—
63	C₄×C₁₃	#456	1	3	yes	—
64	Dic₁₃	—	4	4	no	—
65	Dic₁₃	—	8	6	no	—
66	C₂×Q₁₆	—	26	6	no	—
67	C₂×M₁₆	D₅₂	1	6	yes	—
68	C₄⋊Q₈	—	13	6	no	—
69	#125	—	26	3	no	—
70	C₂²⋊Q₈	—	26	6	no	—
71	C₄×Q₈	—	26	6	no	—
72	#117	—	26	3	no	—
73	C₂×C₄²	—	26	3	no	—
74	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
75	#106	—	26	6	no	—
76	C₄⋊C₈	—	2	6	no	—
77	#103	—	26	12	no	—
78	C₂×C₁₃	—	4	1	no	—
79	C₂×C₁₃	#2007	1	3	yes	—
80	C₂×Q₈	—	26	6	no	—
81	C₂²×C₄	—	52	1	no	—
82	C₂²×C₄	C₂×D₅₂	1	3	yes	—
83	Q₁₆	—	104	6	no	—
84	M₁₆	—	4	6	no	—
85	C₂×C₈	—	2	6	no	—
86	C₄⋊C₄	—	26	6	no	—
87	C₄⋊C₄	—	26	6	no	—
88	C₄⋊C₄	—	52	6	no	—
89	C₂²⋊C₄	—	52	3	no	—
90	C₄²	—	26	6	no	—
91	C₄²	—	52	3	no	—
92	C₄²	—	52	3	no	—
93	C₄²	D₄×D₁₃	1	3	yes	—
94	C₄²	#6131	1	1	yes	characteristic
95	C₁₃	#10303	1	1	yes	characteristic, complemented, Sylow
96	C₂³	#88128	1	1	yes	characteristic
97	Q₈	—	52	6	no	—
98	Q₈	—	52	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	52	6	no	—
102	C₂×C₄	—	52	6	no	—
103	C₂×C₄	#88136	1	3	yes	—
104	C₂×C₄	#88149	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	#11718332	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	52	4	no	—
110	C₄	—	104	6	no	—
111	C₄	#11718407	1	3	yes	—
112	C₄	#11718413	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	#13115885	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13126230

C₂

yes

maximal

#13115812

C₂

yes

maximal

C₁₃×#1309

C₂

yes

maximal, characteristic

#11719175

C₂²

yes

—

C₁₃×#423

C₂²

yes

—

#11718798

—

C₄²×Dic₁₃

C₂²

yes

—

—

—

C₂×C₁₃×M₁₆

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

#88180

—

#88178

—

C₂×C₄×Dic₁₃

—

C₂×Dic₅₂

—

#88124

—

#88123

D₄

yes

—

C₄×Dic₂₆

—

C₁₃×C₄⋊C₈

—

—

—

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

Dic₅₂

—

#3255

—

#1994

—

#1309

D₁₃

yes

characteristic

C₂³×C₁₃

#127

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#120

yes

—

C₂×C₄×C₁₃

#121

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

—

—

—

—

C₂×D₁₃

yes

—

C₄³

—

#339

—

C₂²×C₁₃

—

C₂²×C₁₃

#392

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

#455

yes

—

C₄×C₁₃

#456

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×Q₁₆

—

C₂×M₁₆

D₅₂

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

#106

—

C₄⋊C₈

—

#103

—

C₂×C₁₃

—

C₂×C₁₃

#2007

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×D₅₂

yes

—

Q₁₆

—

104

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

D₄×D₁₃

yes

—

C₄²

#6131

yes

characteristic

C₁₃

#10303

yes

characteristic, complemented, Sylow

C₂³

#88128

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#88136

yes

—

104

C₂×C₄

#88149

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

#11718332

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

104

—

111

C₄

#11718407

yes

—

112

C₄

#11718413

yes

—

113

C₂

—

114

C₂

#13115885

yes

—

	subgroup	G/H
center	C₂²	#11718332
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1309	C₂
socle	C₂²×C₁₃	#392
prime radical	C₂³×C₁₃	#127
hypercenter	#1309	D₁₃
hypocenter	C₁₃	#10303
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#11718332

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1309

C₂

C₂²×C₁₃

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
95. C₁₃	#10303	semidirect

H ≅ G/N

type

95. C₁₃

#10303

semidirect

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

subgroup	index
#13126230	2
#13115812	2
C₁₃×#1309	2
#10303	13

subgroup

index

#13126230

#13115812

C₁₃×#1309

#10303

Subgroups — #15765685

Conjugacy classes of subgroups

Complements

Maximal subgroups