Group #15756647 — subgroups

Subgroups — #15756647

Order 3328.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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	#13112681	C₂	1	2	yes	maximal
2	#13112669	C₂	1	2	yes	maximal
3	#13112667	C₂	1	2	yes	maximal
4	C₁₃×#1745	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
6	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
7	C₄³×C₁₃	C₂²	1	1	yes	characteristic
8	#11718586	C₂²	1	4	yes	—
9	C₁₃×#336	C₄	1	4	yes	—
10	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₃	—	2	2	no	—
13	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
15	C₁₃×#97	—	2	2	no	—
16	C₁₃×#97	—	2	2	no	—
17	C₂²⋊#1055	—	2	4	no	—
18	C₄⋊#1055	—	2	4	no	—
19	C₄×#1055	—	2	4	no	—
20	#8802	—	13	1	no	maximal, Sylow
21	C₂²×C₄×C₁₃	—	2	2	no	—
22	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	#41	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₂×C₈×C₁₃	—	2	2	no	—
26	C₂×C₈×C₁₃	—	2	4	no	—
27	C₂×C₈×C₁₃	—	2	4	no	—
28	C₄²×C₁₃	—	2	4	no	—
29	C₄²×C₁₃	—	4	4	no	—
30	C₄²×C₁₃	#41	1	2	yes	—
31	C₄²×C₁₃	#41	1	2	yes	—
32	C₂×#1055	—	4	4	no	—
33	#1745	D₁₃	1	1	yes	characteristic
34	#1281	—	13	2	no	—
35	#1276	—	13	2	no	—
36	#1275	—	13	2	no	—
37	C₂³×C₁₃	#117	1	1	yes	characteristic
38	C₂×C₄×C₁₃	—	2	4	no	—
39	C₂×C₄×C₁₃	—	4	2	no	—
40	C₂×C₄×C₁₃	—	4	2	no	—
41	C₂×C₄×C₁₃	—	4	2	no	—
42	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
43	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
44	C₂×C₄×C₁₃	#126	1	4	yes	—
45	C₂×C₄×C₁₃	#131	1	4	yes	—
46	C₈×C₁₃	—	4	2	no	—
47	C₈×C₁₃	—	4	2	no	—
48	#1055	—	8	4	no	—
49	#431	—	13	4	no	—
50	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
51	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
52	C₄³	C₂×D₁₃	1	1	yes	characteristic
53	#336	Dic₁₃	1	4	yes	—
54	C₂²×C₁₃	—	2	2	no	—
55	C₂²×C₁₃	#383	1	1	yes	characteristic
56	C₂²×C₁₃	#433	1	2	yes	—
57	C₄×C₁₃	—	2	4	no	—
58	C₄×C₁₃	—	4	4	no	—
59	C₄×C₁₃	#433	1	2	yes	—
60	C₄×C₁₃	#433	1	2	yes	—
61	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
62	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
63	C₂×C₄²	—	2	2	no	—
64	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
65	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
66	C₄⋊C₈	—	26	4	no	—
67	C₂²⋊C₈	—	26	4	no	—
68	#97	—	2	2	no	—
69	#97	—	2	2	no	—
70	C₄×C₈	—	26	4	no	—
71	C₂×C₁₃	—	2	2	no	—
72	C₂×C₁₃	#1840	1	1	yes	characteristic
73	C₂×C₁₃	#1841	1	2	yes	—
74	C₂²×C₄	—	2	2	no	—
75	C₂²×C₄	#6127	1	2	yes	—
76	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	4	no	—
81	C₂×C₈	—	52	4	no	—
82	C₄²	—	2	4	no	—
83	C₄²	—	4	4	no	—
84	C₄²	#6127	1	2	yes	—
85	C₄²	#6127	1	2	yes	—
86	C₁₃	#8802	1	1	yes	characteristic, complemented, Sylow
87	C₂³	#88180	1	1	yes	characteristic
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	4	2	no	—
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	#88130	1	4	yes	—
93	C₂×C₄	#88180	1	1	yes	characteristic
94	C₂×C₄	#88180	1	1	yes	characteristic
95	C₂×C₄	#88202	1	4	yes	—
96	C₈	—	4	2	no	—
97	C₈	—	4	2	no	—
98	C₈	—	104	4	no	—
99	C₂²	—	2	2	no	—
100	C₂²	#11718598	1	1	yes	characteristic
101	C₂²	#11718661	1	2	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	4	4	no	—
104	C₄	#11718661	1	2	yes	—
105	C₄	#11718661	1	2	yes	—
106	C₂	—	2	2	no	—
107	C₂	#13114981	1	1	yes	characteristic
108	C₂	#13114985	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13112681

C₂

yes

maximal

#13112669

C₂

yes

maximal

#13112667

C₂

yes

maximal

C₁₃×#1745

C₂

yes

maximal, characteristic

C₂×C₁₃×#97

C₂²

yes

characteristic

C₂×C₁₃×#97

C₂²

yes

characteristic

C₄³×C₁₃

C₂²

yes

characteristic

#11718586

C₂²

yes

—

C₁₃×#336

C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#97

—

C₁₃×#97

—

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

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

#41

yes

—

C₂×#1055

—

#1745

D₁₃

yes

—

—

—

C₂³×C₁₃

#117

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

C₂×C₄×C₁₃

yes

—

C₂×C₄×C₁₃

#131

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

—

#431

—

C₂×#97

C₂×D₁₃

yes

characteristic

C₂×#97

C₂×D₁₃

yes

characteristic

C₄³

C₂×D₁₃

yes

characteristic

#336

Dic₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

#383

yes

characteristic

C₂²×C₁₃

#433

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#433

yes

—

C₄×C₁₃

#433

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂²×C₈

C₂×Dic₁₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₃

yes

—

C₂×C₄²

C₂²×D₁₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#1840

yes

characteristic

C₂×C₁₃

#1841

yes

—

C₂²×C₄

—

C₂²×C₄

#6127

yes

—

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

#6127

yes

—

C₄²

#6127

yes

—

C₁₃

#8802

yes

characteristic, complemented, Sylow

C₂³

#88180

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#88130

yes

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

—

C₈

—

C₈

—

C₈

—

104

—

C₂²

—

100

C₂²

#11718598

yes

characteristic

101

C₂²

#11718661

yes

—

102

C₄

—

103

C₄

—

104

C₄

#11718661

yes

—

105

C₄

#11718661

yes

—

106

C₂

—

107

C₂

#13114981

yes

characteristic

108

C₂

#13114985

yes

—

	subgroup	G/H
center	C₂×C₄	#88180
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1745	C₂
socle	C₂²×C₁₃	#383
prime radical	C₂³×C₁₃	#117
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1745	D₁₃
hypocenter	C₁₃	#8802
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

subgroup

G/H

center

C₂×C₄

#88180

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1745

C₂

C₂²×C₁₃

C₂³×C₁₃

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1745

N	H ≅ G/N	type
86. C₁₃	#8802	semidirect

H ≅ G/N

type

86. C₁₃

#8802

semidirect

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

subgroup	index
#13112681	2
#13112669	2
#13112667	2
C₁₃×#1745	2
#8802	13

subgroup

index

C₁₃×#1745

Subgroups — #15756647

Conjugacy classes of subgroups

Complements

Maximal subgroups