Group #13112243 — subgroups

Subgroups — C₁₃×#3185 #13112243

Order 1664.

358 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 184 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×#533	C₂	1	2	yes	maximal
2	C₁₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#487	C₂	1	2	yes	maximal, complemented
5	C₁₃×#470	C₂	1	4	yes	maximal
6	C₁₃×#441	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×Q₁₆	C₂²	1	4	yes	—
9	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
10	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₃×#125	—	2	2	no	—
13	C₁₃×C₂²⋊Q₈	—	2	2	no	—
14	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₄×Q₈×C₁₃	—	2	2	no	—
16	C₄×Q₈×C₁₃	C₂²	1	4	yes	—
17	C₁₃×#117	—	2	2	no	—
18	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#106	C₂²	1	4	yes	—
20	C₁₃×#103	C₂²	1	8	yes	—
21	C₁₃×#97	C₂²	1	2	yes	—
22	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₁₃	—	2	2	no	—
25	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
26	C₂²×C₄×C₁₃	D₄	1	2	yes	—
27	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×Q₁₆	—	2	8	no	—
29	C₁₃×M₁₆	—	2	4	no	—
30	C₂×C₈×C₁₃	C₂³	1	2	yes	—
31	C₂×C₈×C₁₃	C₂³	1	2	yes	—
32	C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₁₃×C₄⋊C₄	—	2	2	no	—
35	C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₁₃×C₄⋊C₄	—	2	4	no	—
37	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
38	C₁₃×C₂²⋊C₄	—	2	4	no	—
39	C₄²×C₁₃	—	2	4	no	—
40	C₄²×C₁₃	D₄	1	2	yes	—
41	C₄²×C₁₃	C₂³	1	1	yes	characteristic
42	C₄²×C₁₃	C₂³	1	1	yes	characteristic
43	#3185	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
45	Q₈×C₁₃	—	2	8	no	—
46	Q₈×C₁₃	—	4	4	no	—
47	C₂×C₄×C₁₃	—	2	4	no	—
48	C₂×C₄×C₁₃	—	2	2	no	—
49	C₂×C₄×C₁₃	—	2	4	no	—
50	C₂×C₄×C₁₃	—	2	4	no	—
51	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
54	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
55	C₈×C₁₃	—	2	2	no	—
56	C₈×C₁₃	#41	1	4	yes	—
57	#533	C₂×C₁₃	1	2	yes	—
58	#498	C₂×C₁₃	1	1	yes	characteristic, complemented
59	#494	C₂×C₁₃	1	1	yes	characteristic, complemented
60	#487	C₂×C₁₃	1	2	yes	complemented
61	#470	C₂×C₁₃	1	4	yes	—
62	#441	C₂×C₁₃	1	4	yes	complemented
63	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
64	C₂²×C₁₃	—	2	1	no	—
65	C₂²×C₁₃	—	2	2	no	—
66	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
67	C₄×C₁₃	—	2	1	no	—
68	C₄×C₁₃	—	2	2	no	—
69	C₄×C₁₃	—	4	4	no	—
70	C₄×C₁₃	—	4	4	no	—
71	C₄×C₁₃	#137	1	4	yes	—
72	C₄×C₁₃	C₂×#41	1	2	yes	—
73	C₂×Q₁₆	C₂²×C₁₃	1	4	yes	—
74	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
75	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
76	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
77	#125	—	2	2	no	—
78	C₂²⋊Q₈	—	2	2	no	—
79	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
80	C₄×Q₈	—	2	2	no	—
81	C₄×Q₈	C₂²×C₁₃	1	4	yes	—
82	#117	—	2	2	no	—
83	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
84	#106	C₂²×C₁₃	1	4	yes	—
85	#103	C₂²×C₁₃	1	8	yes	—
86	#97	C₂²×C₁₃	1	2	yes	—
87	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
88	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
89	C₂×C₁₃	—	4	1	no	—
90	C₂×C₁₃	#532	1	1	yes	characteristic
91	C₂×C₁₃	C₂×#137	1	2	yes	—
92	C₂×Q₈	—	2	2	no	—
93	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
94	C₂²×C₄	D₄×C₁₃	1	2	yes	—
95	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
96	Q₁₆	—	2	8	no	—
97	M₁₆	—	2	4	no	—
98	C₂×C₈	C₂³×C₁₃	1	2	yes	—
99	C₂×C₈	C₂³×C₁₃	1	2	yes	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	4	no	—
104	C₄⋊C₄	—	2	4	no	—
105	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
106	C₂²⋊C₄	—	2	4	no	—
107	C₄²	—	2	4	no	—
108	C₄²	D₄×C₁₃	1	2	yes	—
109	C₄²	C₂³×C₁₃	1	1	yes	characteristic
110	C₄²	C₂³×C₁₃	1	1	yes	characteristic
111	C₁₃	#3185	1	1	yes	characteristic, direct product factor, Sylow
112	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
113	Q₈	—	2	8	no	—
114	Q₈	—	4	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
120	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
121	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
122	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₁₃×#41	1	4	yes	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	2	no	—
127	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	4	no	—
131	C₄	—	4	4	no	—
132	C₄	C₁₃×#137	1	4	yes	—
133	C₄	C₂×C₁₃×#41	1	2	yes	—
134	C₂	—	4	1	no	—
135	C₂	C₁₃×#532	1	1	yes	characteristic
136	C₂	C₂×C₁₃×#137	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#533

C₂

yes

maximal

C₁₃×#498

C₂

yes

maximal, characteristic, complemented

C₁₃×#494

C₂

yes

maximal, characteristic, complemented

C₁₃×#487

C₂

yes

maximal, complemented

C₁₃×#470

C₂

yes

maximal

C₁₃×#441

C₂

yes

maximal, complemented

C₄×C₁₃×M₁₆

C₂

yes

maximal, characteristic

C₂×C₁₃×Q₁₆

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

—

C₁₃×C₄⋊Q₈

C₂²

yes

—

C₁₃×C₄⋊Q₈

C₂²

yes

—

C₁₃×#125

—

C₁₃×C₂²⋊Q₈

—

C₁₃×C₂²⋊Q₈

C₂²

yes

—

C₄×Q₈×C₁₃

—

C₄×Q₈×C₁₃

C₂²

yes

—

C₁₃×#117

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×#106

C₂²

yes

—

C₁₃×#103

C₂²

yes

—

C₁₃×#97

C₂²

yes

—

C₄×C₈×C₁₃

C₂²

yes

characteristic

C₄×C₈×C₁₃

C₂²

yes

characteristic

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

C₂³

yes

—

C₂²×C₄×C₁₃

D₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×Q₁₆

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

C₂³

yes

—

C₂×C₈×C₁₃

C₂³

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

C₂³

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

C₂³

yes

characteristic

C₄²×C₁₃

C₂³

yes

characteristic

#3185

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

C₂×D₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂⁴

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

#41

yes

—

#533

C₂×C₁₃

yes

—

#498

C₂×C₁₃

yes

characteristic, complemented

#494

C₂×C₁₃

yes

characteristic, complemented

#487

C₂×C₁₃

yes

complemented

#470

C₂×C₁₃

yes

—

#441

C₂×C₁₃

yes

complemented

C₄×M₁₆

C₂×C₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂²×D₄

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#137

yes

—

C₄×C₁₃

C₂×#41

yes

—

C₂×Q₁₆

C₂²×C₁₃

yes

—

C₂×M₁₆

C₂²×C₁₃

yes

—

C₄⋊Q₈

C₂²×C₁₃

yes

—

C₄⋊Q₈

C₂²×C₁₃

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂²×C₁₃

yes

—

C₄×Q₈

—

C₄×Q₈

C₂²×C₁₃

yes

—

#117

—

C₂×C₄²

C₂²×C₁₃

yes

characteristic

#106

C₂²×C₁₃

yes

—

#103

C₂²×C₁₃

yes

—

#97

C₂²×C₁₃

yes

—

C₄×C₈

C₂²×C₁₃

yes

characteristic

C₄×C₈

C₂²×C₁₃

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

#532

yes

characteristic

C₂×C₁₃

C₂×#137

yes

—

C₂×Q₈

—

C₂×Q₈

C₂³×C₁₃

yes

—

C₂²×C₄

D₄×C₁₃

yes

—

C₂²×C₄

C₂³×C₁₃

yes

characteristic

Q₁₆

—

M₁₆

—

C₂×C₈

C₂³×C₁₃

yes

—

C₂×C₈

C₂³×C₁₃

yes

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

C₂³×C₁₃

yes

—

106

C₂²⋊C₄

—

107

C₄²

—

108

C₄²

D₄×C₁₃

yes

—

109

C₄²

C₂³×C₁₃

yes

characteristic

110

C₄²

C₂³×C₁₃

yes

characteristic

111

C₁₃

#3185

yes

characteristic, direct product factor, Sylow

112

C₂³

C₂×D₄×C₁₃

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₄×C₁₃

yes

—

120

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

121

C₂×C₄

C₂×D₄×C₁₃

yes

—

122

C₂×C₄

C₂⁴×C₁₃

yes

characteristic

123

C₈

—

124

C₈

C₁₃×#41

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂²×D₄×C₁₃

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

C₁₃×#137

yes

—

133

C₄

C₂×C₁₃×#41

yes

—

134

C₂

—

135

C₂

C₁₃×#532

yes

characteristic

136

C₂

C₂×C₁₃×#137

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₃

C₂²×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₁₃

prime radical

C₂³×C₁₃

C₂×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
2. C₁₃×#498	C₂	semidirect
3. C₁₃×#494	C₂	semidirect
4. C₁₃×#487	C₂	semidirect
6. C₁₃×#441	C₂	semidirect
43. #3185	C₁₃	direct (N × H)
58. #498	C₂×C₁₃	semidirect
59. #494	C₂×C₁₃	semidirect
60. #487	C₂×C₁₃	semidirect
62. #441	C₂×C₁₃	semidirect
111. C₁₃	#3185	direct (N × H)

H ≅ G/N

type

2. C₁₃×#498

C₂

semidirect

3. C₁₃×#494

C₂

semidirect

4. C₁₃×#487

C₂

semidirect

6. C₁₃×#441

C₂

semidirect

43. #3185

C₁₃

direct (N × H)

58. #498

C₂×C₁₃

semidirect

59. #494

C₂×C₁₃

semidirect

60. #487

C₂×C₁₃

semidirect

62. #441

C₂×C₁₃

semidirect

111. C₁₃

#3185

direct (N × H)

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

subgroup	index
C₁₃×#533	2
C₁₃×#498	2
C₁₃×#494	2
C₁₃×#487	2
C₁₃×#470	2
C₁₃×#441	2
C₄×C₁₃×M₁₆	2
#3185	13

subgroup

index

C₁₃×#533

C₁₃×#498

C₁₃×#494

C₁₃×#487

C₁₃×#470

C₁₃×#441

C₄×C₁₃×M₁₆

#3185

Subgroups — C₁₃×#3185 #13112243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#3185 #13112243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3185 #13112243