Group #13111024 — subgroups

Subgroups — C₁₃×#1966 #13111024

Order 1664.

292 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 120 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⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#101	C₂	1	4	yes	maximal
4	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₁₃	C₂²	1	2	yes	—
6	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
8	C₁₃×C₄⋊Q₈	—	2	1	no	—
9	C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₁₃×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₁₃×C₄⋊C₄	C₄	1	4	yes	—
12	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊C₈	—	2	2	no	—
14	C₁₃×#101	—	2	8	no	—
15	C₁₃×#97	—	2	1	no	—
16	C₄×C₈×C₁₃	—	2	1	no	—
17	C₂×Q₈×C₁₃	—	2	4	no	—
18	C₂×Q₈×C₁₃	—	2	2	no	—
19	C₂×Q₈×C₁₃	—	2	2	no	—
20	C₂×Q₈×C₁₃	—	2	4	no	—
21	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×M₁₆	—	2	2	no	—
25	C₁₃×M₁₆	—	2	4	no	—
26	C₁₃×M₁₆	D₄	1	4	yes	—
27	C₂×C₈×C₁₃	—	2	2	no	—
28	C₂×C₈×C₁₃	—	2	2	no	—
29	C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₁₃×C₄⋊C₄	—	2	4	no	—
31	C₄²×C₁₃	D₄	1	1	yes	characteristic
32	C₄²×C₁₃	D₄	1	1	yes	characteristic
33	C₄²×C₁₃	D₄	1	2	yes	—
34	#1966	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	Q₈×C₁₃	—	4	4	no	—
37	Q₈×C₁₃	—	4	2	no	—
38	Q₈×C₁₃	—	4	2	no	—
39	C₂×C₄×C₁₃	—	2	4	no	—
40	C₂×C₄×C₁₃	—	2	4	no	—
41	C₂×C₄×C₁₃	—	2	8	no	—
42	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
43	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
44	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₁₃	#41	1	2	yes	—
48	C₈×C₁₃	—	2	4	no	—
49	C₈×C₁₃	—	4	2	no	—
50	C₂×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
51	#423	C₂×C₁₃	1	1	yes	characteristic
52	C₂×#101	C₂×C₁₃	1	4	yes	—
53	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic
54	C₂²×C₁₃	—	2	2	no	—
55	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₁₃	C₄×D₄	1	2	yes	—
57	C₄×C₁₃	—	2	2	no	—
58	C₄×C₁₃	—	4	4	no	—
59	C₄×C₁₃	#101	1	4	yes	complemented
60	C₄×C₁₃	#121	1	2	yes	—
61	C₄×C₁₃	#124	1	1	yes	characteristic
62	C₄×C₁₃	#127	1	1	yes	characteristic
63	C₂²×Q₈	C₂²×C₁₃	1	2	yes	—
64	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
65	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
66	C₄⋊Q₈	—	2	1	no	—
67	C₄⋊Q₈	—	2	1	no	—
68	C₄⋊Q₈	—	2	2	no	—
69	C₂×C₄⋊C₄	C₄×C₁₃	1	4	yes	—
70	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
71	C₄⋊C₈	—	2	2	no	—
72	#101	—	2	8	no	—
73	#97	—	2	1	no	—
74	C₄×C₈	—	2	1	no	—
75	C₂×C₁₃	—	2	2	no	—
76	C₂×C₁₃	#390	1	1	yes	characteristic
77	C₂×C₁₃	C₂×#101	1	2	yes	—
78	C₂×Q₈	—	2	4	no	—
79	C₂×Q₈	—	2	2	no	—
80	C₂×Q₈	—	2	2	no	—
81	C₂×Q₈	—	2	4	no	—
82	C₂²×C₄	C₂×C₄×C₁₃	1	4	yes	—
83	C₂²×C₄	C₂×C₄×C₁₃	1	2	yes	—
84	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	2	4	no	—
87	M₁₆	D₄×C₁₃	1	4	yes	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	2	no	—
90	C₄⋊C₄	—	2	4	no	—
91	C₄⋊C₄	—	2	4	no	—
92	C₄²	D₄×C₁₃	1	1	yes	characteristic
93	C₄²	D₄×C₁₃	1	1	yes	characteristic
94	C₄²	D₄×C₁₃	1	2	yes	—
95	C₁₃	#1966	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
97	Q₈	—	4	4	no	—
98	Q₈	—	4	2	no	—
99	Q₈	—	4	2	no	—
100	C₂×C₄	—	2	4	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
104	C₂×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
105	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
106	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
107	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
108	C₂×C₄	C₁₃×#41	1	2	yes	—
109	C₈	—	2	4	no	—
110	C₈	—	4	2	no	—
111	C₂²	—	2	2	no	—
112	C₂²	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
113	C₂²	C₄×D₄×C₁₃	1	2	yes	—
114	C₄	—	2	2	no	—
115	C₄	—	4	4	no	—
116	C₄	C₁₃×#101	1	4	yes	complemented
117	C₄	C₁₃×#121	1	2	yes	—
118	C₄	C₁₃×#124	1	1	yes	characteristic
119	C₄	C₁₃×#127	1	1	yes	characteristic
120	C₂	—	2	2	no	—
121	C₂	C₁₃×#390	1	1	yes	characteristic
122	C₂	C₂×C₁₃×#101	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₃×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₁₃×#423

C₂

yes

maximal, characteristic

C₂×C₁₃×#101

C₂

yes

maximal

C₄×C₁₃×M₁₆

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₃

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

—

C₂×C₁₃×M₁₆

C₂²

yes

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₂×C₁₃×C₄⋊C₄

C₄

yes

—

C₂×C₄²×C₁₃

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

—

C₁₃×#101

—

C₁₃×#97

—

C₄×C₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂×C₄

yes

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₁₃×M₁₆

—

C₁₃×M₁₆

—

C₁₃×M₁₆

D₄

yes

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

D₄

yes

characteristic

C₄²×C₁₃

D₄

yes

characteristic

C₄²×C₁₃

D₄

yes

—

#1966

C₁₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₂×C₄⋊Q₈

C₂×C₁₃

yes

characteristic

#423

C₂×C₁₃

yes

characteristic

C₂×#101

C₂×C₁₃

yes

—

C₄×M₁₆

C₂×C₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

C₄×D₄

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#101

yes

complemented

C₄×C₁₃

#121

yes

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₂²×Q₈

C₂²×C₁₃

yes

—

C₂×M₁₆

C₂²×C₁₃

yes

—

C₂×M₁₆

C₂²×C₁₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

C₄×C₁₃

yes

—

C₂×C₄²

C₂²×C₁₃

yes

characteristic

C₄⋊C₈

—

#101

—

#97

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

#390

yes

characteristic

C₂×C₁₃

C₂×#101

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₂×C₄×C₁₃

yes

—

C₂²×C₄

C₂×C₄×C₁₃

yes

—

C₂²×C₄

C₂³×C₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

D₄×C₁₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×C₁₃

yes

characteristic

C₄²

D₄×C₁₃

yes

characteristic

C₄²

D₄×C₁₃

yes

—

C₁₃

#1966

yes

characteristic, direct product factor, Sylow

C₂³

C₂²×C₄×C₁₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₁₃×C₂²⋊C₄

yes

—

104

C₂×C₄

C₁₃×C₂²⋊C₄

yes

—

105

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

106

C₂×C₄

C₂×D₄×C₁₃

yes

—

107

C₂×C₄

C₂×D₄×C₁₃

yes

characteristic

108

C₂×C₄

C₁₃×#41

yes

—

109

C₈

—

110

C₈

—

111

C₂²

—

112

C₂²

C₂×C₁₃×C₂²⋊C₄

yes

characteristic

113

C₂²

C₄×D₄×C₁₃

yes

—

114

C₄

—

115

C₄

—

116

C₄

C₁₃×#101

yes

complemented

117

C₄

C₁₃×#121

yes

—

118

C₄

C₁₃×#124

yes

characteristic

119

C₄

C₁₃×#127

yes

characteristic

120

C₂

—

121

C₂

C₁₃×#390

yes

characteristic

122

C₂

C₂×C₁₃×#101

yes

—

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

subgroup

G/H

center, socle

C₂²×C₁₃

C₂×C₂²⋊C₄

commutator

C₂³

C₂²×C₄×C₁₃

Frattini, cosocle

C₂²×C₄

C₂³×C₁₃

prime radical

C₂³×C₁₃

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

N	H ≅ G/N	type
34. #1966	C₁₃	direct (N × H)
59. C₄×C₁₃	#101	semidirect
95. C₁₃	#1966	direct (N × H)
116. C₄	C₁₃×#101	semidirect

H ≅ G/N

type

34. #1966

C₁₃

direct (N × H)

59. C₄×C₁₃

#101

semidirect

95. C₁₃

#1966

direct (N × H)

116. C₄

C₁₃×#101

semidirect

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

subgroup	index
C₂×C₁₃×C₄⋊Q₈	2
C₁₃×#423	2
C₂×C₁₃×#101	2
C₄×C₁₃×M₁₆	2
#1966	13

subgroup

index

C₂×C₁₃×C₄⋊Q₈

C₁₃×#423

C₂×C₁₃×#101

C₄×C₁₃×M₁₆

#1966

Subgroups — C₁₃×#1966 #13111024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C13×#1966 #13111024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1966 #13111024