Group #15699231 — subgroups

Subgroups — C₁₃×#12892 #15699231

Order 3328.

274 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 158 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	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1848	C₂	1	2	yes	maximal
3	C₁₃×#1381	C₂	1	4	yes	maximal
4	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
5	C₂×C₁₃×#108	—	2	2	no	—
6	C₂×C₁₃×#108	C₂²	1	4	yes	—
7	C₁₃×#423	—	2	2	no	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#346	C₄	1	4	yes	—
10	C₂×C₁₃×M₁₆	—	2	4	no	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
13	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	—	2	4	no	—
15	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
16	C₁₃×#108	—	2	8	no	—
17	C₁₃×#108	—	4	4	no	—
18	C₁₃×C₄⋊C₈	—	4	4	no	—
19	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₃	Q₈	1	2	yes	—
21	#12892	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
24	C₁₃×M₁₆	—	4	4	no	—
25	C₁₃×M₁₆	—	4	4	no	—
26	C₂×C₈×C₁₃	—	4	4	no	—
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
29	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	#41	1	4	yes	—
32	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₃	D₈	1	2	yes	—
34	C₁₃×C₁₆	—	2	4	no	—
35	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
36	#1848	C₂×C₁₃	1	2	yes	—
37	#1381	C₂×C₁₃	1	4	yes	—
38	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
39	C₂×C₄×C₁₃	—	4	2	no	—
40	C₂×C₄×C₁₃	#107	1	4	yes	—
41	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₃	#124	1	2	yes	—
43	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
44	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
45	C₈×C₁₃	—	8	4	no	—
46	C₈×C₁₃	#106	1	4	yes	—
47	C₈×C₁₃	#117	1	2	yes	—
48	C₈×C₁₃	#125	1	2	yes	—
49	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
50	C₂×#108	—	2	2	no	—
51	C₂×#108	C₂²×C₁₃	1	4	yes	—
52	#423	—	2	2	no	—
53	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
54	#346	C₄×C₁₃	1	4	yes	—
55	C₂²×C₁₃	—	2	2	no	—
56	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
57	C₂²×C₁₃	#487	1	2	yes	—
58	C₄×C₁₃	—	2	4	no	—
59	C₄×C₁₃	#382	1	1	yes	characteristic
60	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
61	C₄×C₁₃	#486	1	2	yes	—
62	C₂×M₁₆	—	2	4	no	—
63	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
64	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
65	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
66	C₂×C₁₆	—	2	4	no	—
67	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
68	#108	—	2	8	no	—
69	#108	—	4	4	no	—
70	C₄⋊C₈	—	4	4	no	—
71	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
72	C₄×C₈	Q₈×C₁₃	1	2	yes	—
73	C₂×C₁₃	—	2	2	no	—
74	C₂×C₁₃	#1834	1	1	yes	characteristic
75	C₂×C₁₃	#2161	1	2	yes	—
76	C₂²×C₄	C₁₃×Q₁₆	1	2	yes	—
77	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
78	M₁₆	—	4	4	no	—
79	M₁₆	—	4	4	no	—
80	C₂×C₈	—	4	4	no	—
81	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
82	C₂×C₈	C₁₃×SD₁₆	1	4	yes	—
83	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
84	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
85	C₂×C₈	C₁₃×#41	1	4	yes	—
86	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
87	C₄²	C₁₃×D₈	1	2	yes	—
88	C₁₆	—	2	4	no	—
89	C₁₃	#12892	1	1	yes	characteristic, direct product factor, Sylow
90	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
91	C₂×C₄	—	4	2	no	—
92	C₂×C₄	C₁₃×#107	1	4	yes	—
93	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄	C₁₃×#124	1	2	yes	—
95	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
96	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
97	C₈	—	8	4	no	—
98	C₈	C₁₃×#106	1	4	yes	—
99	C₈	C₁₃×#117	1	2	yes	—
100	C₈	C₁₃×#125	1	2	yes	—
101	C₂²	—	2	2	no	—
102	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
103	C₂²	C₁₃×#487	1	2	yes	—
104	C₄	—	2	4	no	—
105	C₄	C₁₃×#382	1	1	yes	characteristic
106	C₄	C₂×C₁₃×#106	1	1	yes	characteristic
107	C₄	C₁₃×#486	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	C₁₃×#1834	1	1	yes	characteristic
110	C₂	C₁₃×#2161	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×#346

C₂

yes

maximal, characteristic

C₁₃×#1848

C₂

yes

maximal

C₁₃×#1381

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₁₃×#108

—

C₂×C₁₃×#108

C₂²

yes

—

C₁₃×#423

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#346

C₄

yes

—

C₂×C₁₃×M₁₆

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

C₂×C₄

yes

—

C₁₃×#108

—

C₁₃×#108

—

C₁₃×C₄⋊C₈

—

C₄×C₈×C₁₃

C₂×C₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

#12892

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

Q₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

SD₁₆

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

D₈

yes

—

C₁₃×C₁₆

—

C₂×#346

C₂×C₁₃

yes

characteristic

#1848

C₂×C₁₃

yes

—

#1381

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#107

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#124

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

C₂×SD₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

#106

yes

—

C₈×C₁₃

#117

yes

—

C₈×C₁₃

#125

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×#108

—

C₂×#108

C₂²×C₁₃

yes

—

#423

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#346

C₄×C₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×#107

yes

characteristic

C₂²×C₁₃

#487

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂×M₁₆

—

C₂²×C₈

D₄×C₁₃

yes

characteristic

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

D₄×C₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₃

yes

—

#108

—

#108

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

C₂×C₁₃

—

C₂×C₁₃

#1834

yes

characteristic

C₂×C₁₃

#2161

yes

—

C₂²×C₄

C₁₃×Q₁₆

yes

—

C₂²×C₄

C₂×D₄×C₁₃

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×SD₁₆

yes

—

C₂×C₈

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

C₂×C₈

C₁₃×#41

yes

—

C₄²

C₁₃×C₄⋊C₄

yes

—

C₄²

C₁₃×D₈

yes

—

C₁₆

—

C₁₃

#12892

yes

characteristic, direct product factor, Sylow

C₂³

C₂×C₁₃×Q₁₆

yes

characteristic

C₂×C₄

—

C₂×C₄

C₁₃×#107

yes

—

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

C₂×C₄

C₁₃×#124

yes

—

C₂×C₄

C₂×C₁₃×D₈

yes

characteristic

C₂×C₄

C₂×C₁₃×SD₁₆

yes

—

C₈

—

C₈

C₁₃×#106

yes

—

C₈

C₁₃×#117

yes

—

100

C₈

C₁₃×#125

yes

—

101

C₂²

—

102

C₂²

C₂×C₁₃×#107

yes

characteristic

103

C₂²

C₁₃×#487

yes

—

104

C₄

—

105

C₄

C₁₃×#382

yes

characteristic

106

C₄

C₂×C₁₃×#106

yes

characteristic

107

C₄

C₁₃×#486

yes

—

108

C₂

—

109

C₂

C₁₃×#1834

yes

characteristic

110

C₂

C₁₃×#2161

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₃

C₂×D₈

commutator

C₂×C₈

C₂²×C₄×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle

C₂²×C₁₃

C₂×#107

prime radical

C₂³×C₁₃

C₂×Q₁₆

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
21. #12892	C₁₃	direct (N × H)
89. C₁₃	#12892	direct (N × H)

H ≅ G/N

type

21. #12892

C₁₃

direct (N × H)

89. C₁₃

#12892

direct (N × H)

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

subgroup	index
C₂×C₁₃×#346	2
C₁₃×#1848	2
C₁₃×#1381	2
#12892	13

subgroup

index

C₂×C₁₃×#346

C₁₃×#1848

C₁₃×#1381

#12892

Subgroups — C₁₃×#12892 #15699231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12892 #15699231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12892 #15699231