Group #15699219 — subgroups

Subgroups — C₁₃×#12880 #15699219

Order 3328.

322 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 182 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×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1374	C₂	1	4	yes	maximal
4	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#376	C₄	1	1	yes	characteristic
10	C₁₃×C₄⋊C₁₆	—	2	4	no	—
11	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₃×C₁₆	—	2	4	no	—
17	C₂×C₁₃×C₁₆	—	2	8	no	—
18	C₁₃×#97	—	2	4	no	—
19	C₁₃×#97	—	2	2	no	—
20	C₄×C₈×C₁₃	—	2	4	no	—
21	C₄×C₈×C₁₃	D₄	1	2	yes	—
22	C₄×C₈×C₁₃	Q₈	1	2	yes	—
23	C₁₃×#95	C₈	1	4	yes	—
24	#12880	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₂×C₈×C₁₃	—	2	2	no	—
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
33	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	#41	1	4	yes	—
36	C₄²×C₁₃	—	2	2	no	—
37	C₄²×C₁₃	—	2	2	no	—
38	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
39	C₄²×C₁₃	M₁₆	1	2	yes	—
40	C₁₃×C₁₆	—	4	4	no	—
41	C₂×C₄⋊C₁₆	C₂×C₁₃	1	2	yes	—
42	#1726	C₂×C₁₃	1	1	yes	characteristic
43	#1374	C₂×C₁₃	1	4	yes	—
44	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₃	—	2	4	no	—
46	C₂×C₄×C₁₃	—	2	4	no	—
47	C₂×C₄×C₁₃	—	2	8	no	—
48	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
49	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₁₃	#117	1	2	yes	—
51	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
53	C₈×C₁₃	—	2	2	no	—
54	C₈×C₁₃	—	2	4	no	—
55	C₈×C₁₃	#124	1	2	yes	—
56	C₈×C₁₃	#125	1	2	yes	—
57	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	—
58	C₂×#97	C₄×C₁₃	1	2	yes	—
59	C₂×#97	C₄×C₁₃	1	1	yes	characteristic
60	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
61	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
62	#376	C₄×C₁₃	1	1	yes	characteristic
63	C₄⋊C₁₆	—	2	4	no	—
64	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
65	C₂²×C₁₃	#431	1	2	yes	—
66	C₂²×C₁₃	#504	1	4	yes	—
67	C₄×C₁₃	—	2	4	no	—
68	C₄×C₁₃	—	4	4	no	—
69	C₄×C₁₃	#382	1	1	yes	characteristic
70	C₄×C₁₃	#423	1	1	yes	characteristic
71	C₄×C₁₃	#432	1	2	yes	—
72	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
73	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
74	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
75	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
76	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
77	C₂×C₁₆	—	2	4	no	—
78	C₂×C₁₆	—	2	8	no	—
79	#97	—	2	4	no	—
80	#97	—	2	2	no	—
81	C₄×C₈	—	2	4	no	—
82	C₄×C₈	D₄×C₁₃	1	2	yes	—
83	C₄×C₈	Q₈×C₁₃	1	2	yes	—
84	#95	C₈×C₁₃	1	4	yes	—
85	C₂×C₁₃	#1831	1	1	yes	characteristic
86	C₂×C₁₃	#2151	1	2	yes	—
87	C₂×C₁₃	#2164	1	4	yes	—
88	C₂²×C₄	C₂×C₈×C₁₃	1	4	yes	—
89	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
90	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
95	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
96	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
97	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
98	C₂×C₈	C₁₃×#41	1	4	yes	—
99	C₄²	—	2	2	no	—
100	C₄²	—	2	2	no	—
101	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
102	C₄²	C₁₃×M₁₆	1	2	yes	—
103	C₁₆	—	4	4	no	—
104	C₁₃	#12880	1	1	yes	characteristic, direct product factor, Sylow
105	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	2	8	no	—
109	C₂×C₄	C₁₃×C₄⋊C₈	1	4	yes	—
110	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄	C₁₃×#117	1	2	yes	—
112	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
113	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	2	4	no	—
116	C₈	C₁₃×#124	1	2	yes	—
117	C₈	C₁₃×#125	1	2	yes	—
118	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
119	C₂²	C₁₃×#431	1	2	yes	—
120	C₂²	C₁₃×#504	1	4	yes	—
121	C₄	—	2	4	no	—
122	C₄	—	4	4	no	—
123	C₄	C₁₃×#382	1	1	yes	characteristic
124	C₄	C₁₃×#423	1	1	yes	characteristic
125	C₄	C₁₃×#432	1	2	yes	—
126	C₂	C₁₃×#1831	1	1	yes	characteristic
127	C₂	C₁₃×#2151	1	2	yes	—
128	C₂	C₁₃×#2164	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊C₁₆

C₂

yes

maximal

C₁₃×#1726

C₂

yes

maximal, characteristic

C₁₃×#1374

C₂

yes

maximal

C₂²×C₁₃×C₁₆

C₂²

yes

—

C₂×C₁₃×#97

C₄

yes

—

C₂×C₁₃×#97

C₄

yes

characteristic

C₂×C₄×C₈×C₁₃

C₂²

yes

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#376

C₄

yes

characteristic

C₁₃×C₄⋊C₁₆

—

C₂²×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₂×C₁₃×C₁₆

—

C₁₃×#97

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₄×C₈×C₁₃

D₄

yes

—

C₄×C₈×C₁₃

Q₈

yes

—

C₁₃×#95

C₈

yes

—

#12880

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₄⋊C₄

yes

—

C₂×C₈×C₁₃

M₁₆

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄²×C₁₃

M₁₆

yes

—

C₁₃×C₁₆

—

C₂×C₄⋊C₁₆

C₂×C₁₃

yes

—

#1726

C₂×C₁₃

yes

characteristic

#1374

C₂×C₁₃

yes

—

C₂³×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₄⋊C₈

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

#117

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

—

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

#124

yes

—

C₈×C₁₃

#125

yes

—

C₂²×C₁₆

C₂²×C₁₃

yes

—

C₂×#97

C₄×C₁₃

yes

—

C₂×#97

C₄×C₁₃

yes

characteristic

C₂×C₄×C₈

C₂²×C₁₃

yes

—

C₂×C₄×C₈

C₂²×C₁₃

yes

characteristic

#376

C₄×C₁₃

yes

characteristic

C₄⋊C₁₆

—

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₃

#431

yes

—

C₂²×C₁₃

#504

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

C₂²×C₈

C₂×C₄×C₁₃

yes

characteristic

C₂²×C₈

C₂×C₄×C₁₃

yes

—

C₂²×C₈

C₂³×C₁₃

yes

characteristic

C₂×C₄²

C₂×C₄×C₁₃

yes

—

C₂×C₄²

C₂×C₄×C₁₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

D₄×C₁₃

yes

—

C₄×C₈

Q₈×C₁₃

yes

—

#95

C₈×C₁₃

yes

—

C₂×C₁₃

#1831

yes

characteristic

C₂×C₁₃

#2151

yes

—

C₂×C₁₃

#2164

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂×C₈×C₁₃

yes

—

C₂²×C₄

C₂²×C₄×C₁₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₁₃×C₄⋊C₄

yes

—

C₂×C₈

C₁₃×M₁₆

yes

—

C₂×C₈

C₂×D₄×C₁₃

yes

characteristic

C₂×C₈

C₂×Q₈×C₁₃

yes

characteristic

C₂×C₈

C₁₃×#41

yes

—

C₄²

—

100

C₄²

—

101

C₄²

C₁₃×C₄⋊C₄

yes

—

102

C₄²

C₁₃×M₁₆

yes

—

103

C₁₆

—

104

C₁₃

#12880

yes

characteristic, direct product factor, Sylow

105

C₂³

C₂²×C₈×C₁₃

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₁₃×C₄⋊C₈

yes

—

110

C₂×C₄

C₂×C₁₃×C₄⋊C₄

yes

characteristic

111

C₂×C₄

C₁₃×#117

yes

—

112

C₂×C₄

C₂×C₁₃×M₁₆

yes

—

113

C₂×C₄

C₂×C₁₃×M₁₆

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

C₁₃×#124

yes

—

117

C₈

C₁₃×#125

yes

—

118

C₂²

C₂×C₁₃×C₄⋊C₈

yes

characteristic

119

C₂²

C₁₃×#431

yes

—

120

C₂²

C₁₃×#504

yes

—

121

C₄

—

122

C₄

—

123

C₄

C₁₃×#382

yes

characteristic

124

C₄

C₁₃×#423

yes

characteristic

125

C₄

C₁₃×#432

yes

—

126

C₂

C₁₃×#1831

yes

characteristic

127

C₂

C₁₃×#2151

yes

—

128

C₂

C₁₃×#2164

yes

—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

subgroup

G/H

center

C₂²×C₈×C₁₃

C₂³

commutator

C₂³

C₂²×C₈×C₁₃

Frattini, cosocle

C₂²×C₈

C₂³×C₁₃

socle, prime radical

C₂³×C₁₃

C₂²×C₈

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂²×C₈×C₁₃ ◁ G

N	H ≅ G/N	type
24. #12880	C₁₃	direct (N × H)
104. C₁₃	#12880	direct (N × H)

H ≅ G/N

type

24. #12880

C₁₃

direct (N × H)

104. C₁₃

#12880

direct (N × H)

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

subgroup	index
C₂×C₁₃×C₄⋊C₁₆	2
C₁₃×#1726	2
C₁₃×#1374	2
#12880	13

subgroup

index

C₂×C₁₃×C₄⋊C₁₆

C₁₃×#1726

C₁₃×#1374

#12880

Subgroups — C₁₃×#12880 #15699219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#12880 #15699219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12880 #15699219