Group #13113560 — subgroups

Subgroups — #13113560

Order 1664.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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	D₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	#11718496	C₂	1	2	yes	maximal
3	C₁₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718138	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718073	C₂	1	2	yes	maximal, complemented
6	C₂×Q₈×D₁₃	C₄	1	2	yes	—
7	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	#88198	C₄	1	2	yes	—
9	C₄⋊C₄×D₁₃	—	2	2	no	—
10	#88142	—	2	2	no	—
11	C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#88123	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	#88060	—	2	2	no	—
15	#88055	—	2	2	no	—
16	C₄⋊#1055	C₂²	1	2	yes	—
17	C₂×Q₈×C₁₃	C₂×C₄	1	2	yes	—
18	Q₈×D₁₃	—	4	4	no	—
19	C₂×C₄×D₁₃	—	2	2	no	—
20	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×D₁₃	D₄	1	2	yes	—
22	C₂×Dic₂₆	—	2	2	no	—
23	C₂×Dic₂₆	C₂×C₄	1	2	yes	—
24	C₂×C₈×C₁₃	—	2	2	no	—
25	C₁₃×C₄⋊C₄	—	2	2	no	—
26	C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₁₃	—	2	2	no	—
28	#6101	—	2	4	no	—
29	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₃	D₄	1	2	yes	—
31	C₂×#1055	—	2	2	no	—
32	#1558	—	13	1	no	maximal, Sylow
33	C₂²×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
34	Q₈×C₁₃	—	4	2	no	—
35	C₂×C₄×C₁₃	—	2	2	no	—
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
38	C₂×Dic₁₃	—	2	2	no	—
39	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
40	C₂×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₄×D₁₃	—	2	2	no	—
42	C₄×D₁₃	—	2	2	no	—
43	C₄×D₁₃	—	2	2	no	—
44	C₄×D₁₃	—	4	4	no	—
45	Dic₂₆	—	4	4	no	—
46	Dic₂₆	—	4	2	no	—
47	C₈×C₁₃	—	4	2	no	—
48	#1055	—	4	2	no	—
49	C₂×C₄⋊Q₈	—	13	1	no	—
50	#432	—	13	2	no	—
51	#333	—	13	1	no	—
52	#333	—	13	2	no	—
53	#333	D₁₃	1	1	yes	characteristic, complemented
54	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×D₁₃	—	2	2	no	—
56	C₂×D₁₃	#100	1	2	yes	—
57	C₄×C₁₃	—	2	1	no	—
58	C₄×C₁₃	—	4	2	no	—
59	C₄×C₁₃	#137	1	2	yes	—
60	C₄×C₁₃	#137	1	2	yes	—
61	Dic₁₃	—	2	1	no	—
62	Dic₁₃	—	2	2	no	—
63	Dic₁₃	—	4	2	no	—
64	C₂²×Q₈	—	13	2	no	—
65	C₄⋊Q₈	—	13	2	no	—
66	C₄⋊Q₈	—	13	1	no	—
67	C₄⋊Q₈	—	26	2	no	—
68	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
69	C₂×C₄⋊C₄	—	26	2	no	—
70	C₂×C₄²	—	13	1	no	—
71	C₄⋊C₈	—	13	2	no	—
72	C₄⋊C₈	C₂×D₁₃	1	2	yes	—
73	C₂²⋊C₈	—	26	2	no	—
74	#97	—	26	2	no	—
75	C₂×C₁₃	C₂×#100	1	1	yes	characteristic
76	C₂×C₁₃	#419	1	2	yes	—
77	D₁₃	—	2	2	no	—
78	C₂×Q₈	—	13	2	no	—
79	C₂×Q₈	—	26	2	no	—
80	C₂×Q₈	—	52	4	no	—
81	C₂×Q₈	C₄×D₁₃	1	2	yes	—
82	C₂²×C₄	—	13	1	no	—
83	C₂²×C₄	—	13	2	no	—
84	C₂²×C₄	—	26	2	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	26	2	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	26	4	no	—
89	C₄⋊C₄	—	26	2	no	—
90	C₄²	—	13	1	no	—
91	C₄²	—	13	2	no	—
92	C₄²	C₂²×D₁₃	1	1	yes	characteristic
93	C₁₃	#1558	1	1	yes	characteristic, complemented, Sylow
94	C₂³	—	13	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	52	2	no	—
97	Q₈	—	52	4	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	13	1	no	—
101	C₂×C₄	—	26	2	no	—
102	C₂×C₄	—	26	2	no	—
103	C₂×C₄	—	26	2	no	—
104	C₂×C₄	—	26	2	no	—
105	C₂×C₄	—	52	4	no	—
106	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
107	C₂×C₄	D₄×D₁₃	1	2	yes	—
108	C₈	—	4	2	no	—
109	C₈	—	52	2	no	—
110	C₂²	—	13	2	no	—
111	C₂²	—	26	2	no	—
112	C₂²	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	4	2	no	—
115	C₄	—	26	1	no	—
116	C₄	—	26	2	no	—
117	C₄	—	52	2	no	—
118	C₄	#88169	1	2	yes	—
119	C₄	#88172	1	2	yes	—
120	C₂	—	26	2	no	—
121	C₂	D₁₃×#100	1	1	yes	characteristic
122	C₂	#11718463	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₁₃×C₄⋊Q₈

C₂

yes

maximal, characteristic

#11718496

C₂

yes

maximal

C₁₃×#333

C₂

yes

maximal, characteristic, complemented

#11718138

C₂

yes

maximal, characteristic, complemented

#11718073

C₂

yes

maximal, complemented

C₂×Q₈×D₁₃

C₄

yes

—

C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

#88198

C₄

yes

—

C₄⋊C₄×D₁₃

—

#88142

—

C₄²×D₁₃

C₂²

yes

characteristic

#88123

C₂²

yes

characteristic

C₁₃×C₄⋊C₈

C₂²

yes

—

#88060

—

#88055

—

C₄⋊#1055

C₂²

yes

—

C₂×Q₈×C₁₃

C₂×C₄

yes

—

Q₈×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₄×D₁₃

D₄

yes

—

C₂×Dic₂₆

—

C₂×Dic₂₆

C₂×C₄

yes

—

C₂×C₈×C₁₃

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂³

yes

characteristic

C₄⋊Dic₁₃

—

#6101

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

C₂×#1055

—

#1558

—

maximal, Sylow

C₂²×D₁₃

C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

C₂²⋊C₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

—

#1055

—

C₂×C₄⋊Q₈

—

—

—

—

D₁₃

yes

characteristic, complemented

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#100

yes

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#137

yes

—

C₄×C₁₃

#137

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₂²×Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₁₃

yes

—

C₂²⋊C₈

—

#97

—

C₂×C₁₃

C₂×#100

yes

characteristic

C₂×C₁₃

#419

yes

—

D₁₃

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₄×D₁₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²×D₁₃

yes

characteristic

C₁₃

#1558

yes

characteristic, complemented, Sylow

C₂³

—

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

C₂×C₄×D₁₃

yes

characteristic

107

C₂×C₄

D₄×D₁₃

yes

—

108

C₈

—

109

C₈

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂²⋊C₄×D₁₃

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#88169

yes

—

119

C₄

#88172

yes

—

120

C₂

—

121

C₂

D₁₃×#100

yes

characteristic

122

C₂

#11718463

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#333	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂³
hypercenter	#333	D₁₃
hypocenter	C₁₃	#1558
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#333

C₂

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂²×D₁₃

C₂²⋊C₄

cosocle

C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
3. C₁₃×#333	C₂	semidirect
4. #11718138	C₂	semidirect
5. #11718073	C₂	semidirect
53. #333	D₁₃	semidirect
93. C₁₃	#1558	semidirect

H ≅ G/N

type

3. C₁₃×#333

C₂

semidirect

4. #11718138

C₂

semidirect

5. #11718073

C₂

semidirect

53. #333

D₁₃

semidirect

93. C₁₃

#1558

semidirect

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

subgroup	index
D₁₃×C₄⋊Q₈	2
#11718496	2
C₁₃×#333	2
#11718138	2
#11718073	2
#1558	13

subgroup

index

D₁₃×C₄⋊Q₈

C₁₃×#333

Subgroups — #13113560

Conjugacy classes of subgroups

Complements

Maximal subgroups