Group #15696699 — subgroups

Subgroups — C₁₃×#10360 #15696699

Order 3328.

476 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₁₃×#2845	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#1961	C₂	1	3	yes	maximal
3	C₁₃×#1295	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×#102	—	2	6	no	—
6	C₂×C₁₃×#97	C₂²	1	3	yes	—
7	C₁₃×#398	—	2	6	no	—
8	C₁₃×#382	C₂²	1	3	yes	—
9	C₂²×D₄×C₁₃	—	2	3	no	—
10	C₂²×C₈×C₁₃	—	2	3	no	—
11	C₁₃×#127	—	2	3	no	—
12	C₁₃×#127	Q₈	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
14	C₂×C₁₃×C₄⋊C₄	D₄	1	6	yes	—
15	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
16	C₁₃×#102	—	4	12	no	—
17	C₁₃×#97	—	2	6	no	—
18	C₁₃×#95	—	2	2	no	—
19	C₁₃×#95	—	2	6	no	—
20	#10360	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂⁴×C₁₃	—	4	1	no	—
22	C₂×D₄×C₁₃	—	2	6	no	—
23	C₂×D₄×C₁₃	—	4	6	no	—
24	C₂×D₄×C₁₃	—	4	6	no	—
25	C₂×D₄×C₁₃	—	4	3	no	—
26	C₂²×C₄×C₁₃	—	2	6	no	—
27	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
28	C₂×C₈×C₁₃	—	2	6	no	—
29	C₂×C₈×C₁₃	—	4	3	no	—
30	C₂×C₈×C₁₃	—	4	3	no	—
31	C₁₃×C₄⋊C₄	—	4	6	no	—
32	C₁₃×C₄⋊C₄	—	8	6	no	—
33	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₄²×C₁₃	#41	1	3	yes	—
35	#2845	C₂×C₁₃	1	1	yes	characteristic, complemented
36	#1961	C₂×C₁₃	1	3	yes	—
37	#1295	C₂×C₁₃	1	3	yes	complemented
38	C₂³×C₁₃	—	4	2	no	—
39	C₂³×C₁₃	—	8	3	no	—
40	C₂³×C₁₃	—	8	3	no	—
41	C₂³×C₁₃	#120	1	1	yes	characteristic
42	D₄×C₁₃	—	4	12	no	—
43	D₄×C₁₃	—	8	6	no	—
44	C₂×C₄×C₁₃	—	2	3	no	—
45	C₂×C₄×C₁₃	—	2	3	no	—
46	C₂×C₄×C₁₃	—	4	6	no	—
47	C₂×C₄×C₁₃	—	4	6	no	—
48	C₂×C₄×C₁₃	—	4	6	no	—
49	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
50	C₂×C₄×C₁₃	#124	1	3	yes	—
51	C₈×C₁₃	—	4	6	no	—
52	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
53	C₂×#102	—	2	6	no	—
54	C₂×#97	C₂²×C₁₃	1	3	yes	—
55	#398	—	2	6	no	—
56	#382	C₂²×C₁₃	1	3	yes	—
57	C₂²×C₁₃	—	8	6	no	—
58	C₂²×C₁₃	—	16	3	no	—
59	C₂²×C₁₃	—	16	1	no	—
60	C₂²×C₁₃	#393	1	1	yes	characteristic
61	C₂²×C₁₃	#453	1	3	yes	—
62	C₂²×C₁₃	#454	1	3	yes	—
63	C₄×C₁₃	—	2	3	no	—
64	C₄×C₁₃	—	2	3	no	—
65	C₄×C₁₃	—	8	6	no	—
66	C₂²×D₄	—	2	3	no	—
67	C₂²×C₈	—	2	3	no	—
68	#127	—	2	3	no	—
69	#127	Q₈×C₁₃	1	2	yes	—
70	C₂×C₄⋊C₄	—	2	6	no	—
71	C₂×C₄⋊C₄	D₄×C₁₃	1	6	yes	—
72	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
73	#102	—	4	12	no	—
74	#97	—	2	6	no	—
75	#95	—	2	2	no	—
76	#95	—	2	6	no	—
77	C₂×C₁₃	—	16	2	no	—
78	C₂×C₁₃	#1656	1	3	yes	—
79	C₂×C₁₃	#1658	1	1	yes	characteristic
80	C₂×C₁₃	#2027	1	3	yes	—
81	C₂⁴	—	4	1	no	—
82	C₂×D₄	—	2	6	no	—
83	C₂×D₄	—	4	6	no	—
84	C₂×D₄	—	4	6	no	—
85	C₂×D₄	—	4	3	no	—
86	C₂²×C₄	—	2	6	no	—
87	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
88	C₂×C₈	—	2	6	no	—
89	C₂×C₈	—	4	3	no	—
90	C₂×C₈	—	4	3	no	—
91	C₄⋊C₄	—	4	6	no	—
92	C₄⋊C₄	—	8	6	no	—
93	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
94	C₄²	C₁₃×#41	1	3	yes	—
95	C₁₃	#10360	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	—	4	2	no	—
97	C₂³	—	8	3	no	—
98	C₂³	—	8	3	no	—
99	C₂³	C₁₃×#120	1	1	yes	characteristic
100	D₄	—	4	12	no	—
101	D₄	—	8	6	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	4	6	no	—
105	C₂×C₄	—	4	6	no	—
106	C₂×C₄	—	4	6	no	—
107	C₂×C₄	C₁₃×C₂²⋊Q₈	1	3	yes	—
108	C₂×C₄	C₁₃×#124	1	3	yes	—
109	C₈	—	4	6	no	—
110	C₂²	—	8	6	no	—
111	C₂²	—	16	3	no	—
112	C₂²	—	16	1	no	—
113	C₂²	C₁₃×#393	1	1	yes	characteristic
114	C₂²	C₁₃×#453	1	3	yes	—
115	C₂²	C₁₃×#454	1	3	yes	—
116	C₄	—	2	3	no	—
117	C₄	—	2	3	no	—
118	C₄	—	8	6	no	—
119	C₂	—	16	2	no	—
120	C₂	C₁₃×#1656	1	3	yes	—
121	C₂	C₁₃×#1658	1	1	yes	characteristic
122	C₂	C₁₃×#2027	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2845

C₂

yes

maximal, characteristic, complemented

C₁₃×#1961

C₂

yes

maximal

C₁₃×#1295

C₂

yes

maximal, complemented

C₂×C₁₃×#127

C₂²

yes

characteristic

C₂×C₁₃×#102

—

C₂×C₁₃×#97

C₂²

yes

—

C₁₃×#398

—

C₁₃×#382

C₂²

yes

—

C₂²×D₄×C₁₃

—

C₂²×C₈×C₁₃

—

C₁₃×#127

—

C₁₃×#127

Q₈

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#102

—

C₁₃×#97

—

C₁₃×#95

—

C₁₃×#95

—

#10360

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂⁴×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

#2845

C₂×C₁₃

yes

characteristic, complemented

#1961

C₂×C₁₃

yes

—

#1295

C₂×C₁₃

yes

complemented

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#120

yes

characteristic

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

#124

yes

—

C₈×C₁₃

—

C₂×#127

C₂²×C₁₃

yes

characteristic

C₂×#102

—

C₂×#97

C₂²×C₁₃

yes

—

#398

—

#382

C₂²×C₁₃

yes

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#393

yes

characteristic

C₂²×C₁₃

#453

yes

—

C₂²×C₁₃

#454

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

Q₈×C₁₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄²

C₂³×C₁₃

yes

—

—

—

—

C₂×C₁₃

—

C₂×C₁₃

#1656

yes

—

C₂×C₁₃

#1658

yes

characteristic

C₂×C₁₃

#2027

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×Q₈×C₁₃

yes

characteristic

C₄²

C₁₃×#41

yes

—

C₁₃

#10360

yes

characteristic, direct product factor, Sylow

C₂³

—

C₂³

—

C₂³

—

C₂³

C₁₃×#120

yes

characteristic

100

D₄

—

101

D₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

108

C₂×C₄

C₁₃×#124

yes

—

109

C₈

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₁₃×#393

yes

characteristic

114

C₂²

C₁₃×#453

yes

—

115

C₂²

C₁₃×#454

yes

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₂

—

120

C₂

C₁₃×#1656

yes

—

121

C₂

C₁₃×#1658

yes

characteristic

122

C₂

C₁₃×#2027

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

prime radical

C₂×C₁₃×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
1. C₁₃×#2845	C₂	semidirect
3. C₁₃×#1295	C₂	semidirect
20. #10360	C₁₃	direct (N × H)
35. #2845	C₂×C₁₃	semidirect
37. #1295	C₂×C₁₃	semidirect
95. C₁₃	#10360	direct (N × H)

H ≅ G/N

type

1. C₁₃×#2845

C₂

semidirect

3. C₁₃×#1295

C₂

semidirect

20. #10360

C₁₃

direct (N × H)

35. #2845

C₂×C₁₃

semidirect

37. #1295

C₂×C₁₃

semidirect

95. C₁₃

#10360

direct (N × H)

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

subgroup	index
C₁₃×#2845	2
C₁₃×#1961	2
C₁₃×#1295	2
#10360	13

subgroup

index

C₁₃×#2845

C₁₃×#1961

C₁₃×#1295

#10360

Subgroups — C₁₃×#10360 #15696699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10360 #15696699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10360 #15696699