Group #15696922 — subgroups

Subgroups — C₁₃×#10583 #15696922

Order 3328.

406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2844	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1847	C₂	1	3	yes	maximal
3	C₁₃×#1295	C₂	1	3	yes	maximal
4	C₂×C₁₃×#107	—	2	3	no	—
5	C₂×C₁₃×#106	—	2	3	no	—
6	C₂×C₁₃×#97	C₂²	1	3	yes	—
7	C₁₃×#400	—	2	3	no	—
8	C₁₃×#395	—	2	3	no	—
9	C₁₃×#384	C₂²	1	1	yes	characteristic
10	C₁₃×#382	C₂²	1	3	yes	—
11	C₂²×Q₈×C₁₃	—	2	1	no	—
12	C₂²×C₈×C₁₃	—	2	3	no	—
13	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
14	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
15	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
16	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
17	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
18	C₁₃×#107	—	4	6	no	—
19	C₁₃×#106	—	4	6	no	—
20	C₁₃×#97	—	2	3	no	—
21	C₁₃×#97	Q₈	1	6	yes	complemented
22	C₁₃×#95	—	2	3	no	—
23	C₁₃×#95	—	2	1	no	—
24	C₁₃×#95	—	2	6	no	—
25	#10583	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂×Q₈×C₁₃	—	8	3	no	—
27	C₂²×C₄×C₁₃	—	2	3	no	—
28	C₂²×C₄×C₁₃	—	2	3	no	—
29	C₂²×C₄×C₁₃	—	4	1	no	—
30	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
31	C₂×C₈×C₁₃	—	2	6	no	—
32	C₂×C₈×C₁₃	—	2	6	no	—
33	C₂×C₈×C₁₃	—	2	6	no	—
34	C₁₃×C₄⋊C₄	—	4	3	no	—
35	C₁₃×C₄⋊C₄	—	4	3	no	—
36	C₁₃×C₄⋊C₄	—	4	3	no	—
37	C₁₃×C₄⋊C₄	—	4	3	no	—
38	C₁₃×C₄⋊C₄	—	8	3	no	—
39	C₄²×C₁₃	C₂×Q₈	1	3	yes	—
40	C₄²×C₁₃	#41	1	1	yes	characteristic
41	#2844	C₂×C₁₃	1	1	yes	characteristic
42	#1847	C₂×C₁₃	1	3	yes	—
43	#1295	C₂×C₁₃	1	3	yes	—
44	C₂³×C₁₃	#120	1	1	yes	characteristic
45	Q₈×C₁₃	—	8	4	no	—
46	C₂×C₄×C₁₃	—	2	3	no	—
47	C₂×C₄×C₁₃	—	2	3	no	—
48	C₂×C₄×C₁₃	—	4	3	no	—
49	C₂×C₄×C₁₃	—	4	3	no	—
50	C₂×C₄×C₁₃	—	4	6	no	—
51	C₂×C₄×C₁₃	—	4	6	no	—
52	C₂×C₄×C₁₃	—	8	3	no	—
53	C₂×C₄×C₁₃	C₂²⋊Q₈	1	3	yes	—
54	C₂×C₄×C₁₃	C₄⋊Q₈	1	3	yes	—
55	C₈×C₁₃	—	2	12	no	—
56	C₂×#107	—	2	3	no	—
57	C₂×#106	—	2	3	no	—
58	C₂×#97	C₂²×C₁₃	1	3	yes	—
59	#400	—	2	3	no	—
60	#395	—	2	3	no	—
61	#384	C₂²×C₁₃	1	1	yes	characteristic
62	#382	C₂²×C₁₃	1	3	yes	—
63	C₂²×C₁₃	#395	1	1	yes	characteristic
64	C₂²×C₁₃	#453	1	3	yes	—
65	C₂²×C₁₃	#456	1	3	yes	—
66	C₄×C₁₃	—	2	3	no	—
67	C₄×C₁₃	—	2	3	no	—
68	C₄×C₁₃	—	8	3	no	—
69	C₄×C₁₃	—	8	3	no	—
70	C₄×C₁₃	—	16	1	no	—
71	C₂²×Q₈	—	2	1	no	—
72	C₂²×C₈	—	2	3	no	—
73	C₂×C₄⋊C₄	—	2	3	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
76	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
77	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
78	#107	—	4	6	no	—
79	#106	—	4	6	no	—
80	#97	—	2	3	no	—
81	#97	Q₈×C₁₃	1	6	yes	complemented
82	#95	—	2	3	no	—
83	#95	—	2	1	no	—
84	#95	—	2	6	no	—
85	C₂×C₁₃	#1655	1	1	yes	characteristic
86	C₂×C₁₃	#1660	1	3	yes	—
87	C₂×C₁₃	#2060	1	3	yes	—
88	C₂×Q₈	—	8	3	no	—
89	C₂²×C₄	—	2	3	no	—
90	C₂²×C₄	—	2	3	no	—
91	C₂²×C₄	—	4	1	no	—
92	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
93	C₂×C₈	—	2	6	no	—
94	C₂×C₈	—	2	6	no	—
95	C₂×C₈	—	2	6	no	—
96	C₄⋊C₄	—	4	3	no	—
97	C₄⋊C₄	—	4	3	no	—
98	C₄⋊C₄	—	4	3	no	—
99	C₄⋊C₄	—	4	3	no	—
100	C₄⋊C₄	—	8	3	no	—
101	C₄²	C₂×Q₈×C₁₃	1	3	yes	—
102	C₄²	C₁₃×#41	1	1	yes	characteristic
103	C₁₃	#10583	1	1	yes	characteristic, direct product factor, Sylow
104	C₂³	C₁₃×#120	1	1	yes	characteristic
105	Q₈	—	8	4	no	—
106	C₂×C₄	—	2	3	no	—
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	4	3	no	—
109	C₂×C₄	—	4	3	no	—
110	C₂×C₄	—	4	6	no	—
111	C₂×C₄	—	4	6	no	—
112	C₂×C₄	—	8	3	no	—
113	C₂×C₄	C₁₃×C₂²⋊Q₈	1	3	yes	—
114	C₂×C₄	C₁₃×C₄⋊Q₈	1	3	yes	—
115	C₈	—	2	12	no	—
116	C₂²	C₁₃×#395	1	1	yes	characteristic
117	C₂²	C₁₃×#453	1	3	yes	—
118	C₂²	C₁₃×#456	1	3	yes	—
119	C₄	—	2	3	no	—
120	C₄	—	2	3	no	—
121	C₄	—	8	3	no	—
122	C₄	—	8	3	no	—
123	C₄	—	16	1	no	—
124	C₂	C₁₃×#1655	1	1	yes	characteristic
125	C₂	C₁₃×#1660	1	3	yes	—
126	C₂	C₁₃×#2060	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#2844

C₂

yes

maximal, characteristic

C₁₃×#1847

C₂

yes

maximal

C₁₃×#1295

C₂

yes

maximal

C₂×C₁₃×#107

—

C₂×C₁₃×#106

—

C₂×C₁₃×#97

C₂²

yes

—

C₁₃×#400

—

C₁₃×#395

—

C₁₃×#384

C₂²

yes

characteristic

C₁₃×#382

C₂²

yes

—

C₂²×Q₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₁₃×#107

—

C₁₃×#106

—

C₁₃×#97

—

C₁₃×#97

Q₈

yes

complemented

C₁₃×#95

—

C₁₃×#95

—

C₁₃×#95

—

#10583

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×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

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

—

C₄²×C₁₃

#41

yes

characteristic

#2844

C₂×C₁₃

yes

characteristic

#1847

C₂×C₁₃

yes

—

#1295

C₂×C₁₃

yes

—

C₂³×C₁₃

#120

yes

characteristic

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×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

C₄⋊Q₈

yes

—

C₈×C₁₃

—

C₂×#107

—

C₂×#106

—

C₂×#97

C₂²×C₁₃

yes

—

#400

—

#395

—

#384

C₂²×C₁₃

yes

characteristic

#382

C₂²×C₁₃

yes

—

C₂²×C₁₃

#395

yes

characteristic

C₂²×C₁₃

#453

yes

—

C₂²×C₁₃

#456

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₂²×Q₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄⋊C₄

D₄×C₁₃

yes

—

C₂×C₄²

C₂³×C₁₃

yes

—

—

—

Q₈×C₁₃

yes

—

—

—

C₂×C₁₃

#1655

yes

characteristic

C₂×C₁₃

#1660

yes

—

C₂×C₁₃

#2060

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

C₂×Q₈×C₁₃

yes

—

102

C₄²

C₁₃×#41

yes

characteristic

103

C₁₃

#10583

yes

characteristic, direct product factor, Sylow

104

C₂³

C₁₃×#120

yes

characteristic

105

Q₈

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

C₁₃×C₂²⋊Q₈

yes

—

114

C₂×C₄

C₁₃×C₄⋊Q₈

yes

—

115

C₈

—

116

C₂²

C₁₃×#395

yes

characteristic

117

C₂²

C₁₃×#453

yes

—

118

C₂²

C₁₃×#456

yes

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₂

C₁₃×#1655

yes

characteristic

125

C₂

C₁₃×#1660

yes

—

126

C₂

C₁₃×#2060

yes

—

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

subgroup

G/H

center, socle, prime radical

C₂³×C₁₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₃

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
21. C₁₃×#97	Q₈	semidirect
25. #10583	C₁₃	direct (N × H)
81. #97	Q₈×C₁₃	semidirect
103. C₁₃	#10583	direct (N × H)

H ≅ G/N

type

21. C₁₃×#97

Q₈

semidirect

25. #10583

C₁₃

direct (N × H)

81. #97

Q₈×C₁₃

semidirect

103. C₁₃

#10583

direct (N × H)

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

subgroup	index
C₁₃×#2844	2
C₁₃×#1847	2
C₁₃×#1295	2
#10583	13

subgroup

index

C₁₃×#2844

C₁₃×#1847

C₁₃×#1295

#10583

Subgroups — C₁₃×#10583 #15696922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#10583 #15696922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10583 #15696922