Group #13130750 — subgroups

Subgroups — #13130750

Order 1664.

236 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 62 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	#11719221	C₂	1	1	yes	maximal, characteristic
2	C₂×#88113	C₂	1	2	yes	maximal
3	#11718239	C₂	1	4	yes	maximal
4	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
5	C₂×#6122	C₂²	1	4	yes	—
6	C₁₃×#117	C₄	1	1	yes	characteristic
7	#88180	C₄	1	1	yes	characteristic
8	#88141	—	2	2	no	—
9	#88131	C₄	1	2	yes	—
10	#88131	C₂²	1	2	yes	—
11	C₄×Dic₂₆	—	2	2	no	—
12	#88113	—	2	2	no	—
13	#88113	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₂₆	—	2	4	no	—
18	C₂×Dic₂₆	D₄	1	2	yes	—
19	C₂×Dic₂₆	D₄	1	2	yes	—
20	#6122	—	2	4	no	—
21	#6122	—	2	4	no	—
22	C₂×#1057	—	2	4	no	—
23	C₁₃×C₄⋊C₄	—	2	1	no	—
24	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
25	C₄²×C₁₃	—	2	1	no	—
26	C₂²⋊Dic₁₃	C₂×C₄	1	2	yes	—
27	C₄⋊Dic₁₃	—	2	1	no	—
28	#6101	—	2	2	no	—
29	#6101	—	2	2	no	—
30	C₄×Dic₁₃	—	2	1	no	—
31	C₄×Dic₁₃	—	2	2	no	—
32	C₄×Dic₁₃	—	2	2	no	—
33	#1830	—	13	1	no	maximal, Sylow
34	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	—	2	2	no	—
37	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₁₃	—	2	2	no	—
40	C₂×Dic₁₃	—	2	2	no	—
41	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
42	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
43	C₂×Dic₁₃	#41	1	4	yes	—
44	Dic₂₆	—	2	4	no	—
45	Dic₂₆	—	2	4	no	—
46	#1057	—	4	4	no	—
47	#519	—	13	1	no	—
48	C₂×#101	—	13	2	no	—
49	#344	—	13	4	no	—
50	C₂²×C₁₃	—	4	1	no	—
51	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₁₃	#117	1	2	yes	—
53	C₄×C₁₃	—	2	1	no	—
54	C₄×C₁₃	—	2	1	no	—
55	C₄×C₁₃	—	4	2	no	—
56	Dic₁₃	—	2	2	no	—
57	Dic₁₃	—	4	2	no	—
58	Dic₁₃	#123	1	4	yes	—
59	C₂²×Q₈	—	13	1	no	—
60	C₂×M₁₆	—	13	4	no	—
61	C₄×Q₈	—	26	2	no	—
62	C₄×Q₈	—	26	2	no	—
63	#117	—	13	1	no	—
64	#117	—	13	2	no	—
65	#117	—	13	2	no	—
66	#117	#261	1	1	yes	characteristic
67	#101	—	26	2	no	—
68	#101	—	26	2	no	—
69	C₂×C₁₃	—	2	1	no	—
70	C₂×C₁₃	—	2	2	no	—
71	C₂×C₁₃	#381	1	1	yes	characteristic
72	C₂×Q₈	—	13	2	no	—
73	C₂×Q₈	—	13	2	no	—
74	C₂×Q₈	—	26	4	no	—
75	C₂²×C₄	—	13	1	no	—
76	C₂²×C₄	—	13	1	no	—
77	C₂²×C₄	C₂×#261	1	1	yes	characteristic
78	M₁₆	—	26	4	no	—
79	M₁₆	—	26	4	no	—
80	C₂×C₈	—	26	4	no	—
81	C₄⋊C₄	—	2	1	no	—
82	C₄⋊C₄	—	26	2	no	—
83	C₄⋊C₄	—	26	2	no	—
84	C₄⋊C₄	—	26	1	no	—
85	C₂²⋊C₄	—	13	2	no	—
86	C₂²⋊C₄	C₂×#261	1	2	yes	—
87	C₄²	—	2	1	no	—
88	C₄²	—	26	2	no	—
89	C₄²	—	26	2	no	—
90	C₄²	—	26	1	no	—
91	C₁₃	#1830	1	1	yes	characteristic, complemented, Sylow
92	C₂³	C₂²×#261	1	1	yes	characteristic
93	Q₈	—	26	4	no	—
94	Q₈	—	26	4	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	13	4	no	—
98	C₂×C₄	—	13	2	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	26	2	no	—
101	C₂×C₄	—	26	2	no	—
102	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
103	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
104	C₈	—	52	4	no	—
105	C₂²	—	4	1	no	—
106	C₂²	#88237	1	2	yes	—
107	C₂²	C₂×C₂²⋊#261	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	4	2	no	—
111	C₄	—	13	4	no	—
112	C₄	—	26	2	no	—
113	C₄	—	52	2	no	—
114	C₂	—	2	1	no	—
115	C₂	—	2	2	no	—
116	C₂	#11719135	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11719221

C₂

yes

maximal, characteristic

C₂×#88113

C₂

yes

maximal

#11718239

C₂

yes

maximal

C₂²×Dic₂₆

C₂²

yes

characteristic

C₂×#6122

C₂²

yes

—

C₁₃×#117

C₄

yes

characteristic

#88180

C₄

yes

characteristic

#88141

—

#88131

C₄

yes

—

#88131

C₂²

yes

—

C₄×Dic₂₆

—

#88113

—

#88113

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

C₂³

yes

characteristic

C₂×Dic₂₆

—

C₂×Dic₂₆

D₄

yes

—

C₂×Dic₂₆

D₄

yes

—

#6122

—

#6122

—

C₂×#1057

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

C₂×C₄

yes

—

C₄²×C₁₃

—

C₂²⋊Dic₁₃

C₂×C₄

yes

—

C₄⋊Dic₁₃

—

#6101

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

#1830

—

maximal, Sylow

C₂³×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

#41

yes

—

Dic₂₆

—

Dic₂₆

—

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₃

#117

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#123

yes

—

C₂²×Q₈

—

C₂×M₁₆

—

C₄×Q₈

—

C₄×Q₈

—

—

—

—

yes

—

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#381

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×#261

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1830

yes

characteristic, complemented, Sylow

C₂³

C₂²×#261

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₂²⋊#261

yes

characteristic

103

C₂×C₄

C₂²⋊#261

yes

characteristic

104

C₈

—

105

C₂²

—

106

C₂²

#88237

yes

—

107

C₂²

C₂×C₂²⋊#261

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₂

—

115

C₂

—

116

C₂

#11719135

yes

characteristic

	subgroup	G/H
center	C₂	#11719135
commutator, prime radical	C₂³×C₁₃	C₂²×C₄
Frattini	C₂³	C₂²×#261
Fitting	C₁₃×#117	C₄
socle	C₂×C₁₃	#381
cosocle	C₂²×Dic₁₃	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#1830
LCS	G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #117

subgroup

G/H

center

C₂

#11719135

commutator, prime radical

C₂³×C₁₃

C₂²×C₄

Frattini

C₂³

C₂²×#261

Fitting

C₁₃×#117

C₄

socle

C₂×C₁₃

#381

cosocle

C₂²×Dic₁₃

C₂³

C₁₃

G ▷ C₂³×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ #117

N	H ≅ G/N	type
91. C₁₃	#1830	semidirect

H ≅ G/N

type

91. C₁₃

#1830

semidirect

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

subgroup	index
#11719221	2
C₂×#88113	2
#11718239	2
#1830	13

subgroup

index

Subgroups — #13130750

Conjugacy classes of subgroups

Complements

Maximal subgroups