Group #11719356 — subgroups

Subgroups — #11719356

Order 832.

196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×#123	C₂	1	1	yes	maximal, characteristic
2	#88190	C₂	1	1	yes	maximal, characteristic
3	#88189	C₂	1	1	yes	maximal, characteristic
4	#88178	C₂	1	2	yes	maximal, complemented
5	#88143	C₂	1	2	yes	maximal, complemented
6	#88142	C₂	1	2	yes	maximal, complemented
7	#88133	C₂	1	2	yes	maximal, complemented
8	#88133	C₂	1	2	yes	maximal, complemented
9	#88132	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₆	C₂²	1	2	yes	—
14	C₂×Dic₂₆	C₂²	1	1	yes	characteristic
15	C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²⋊Dic₁₃	C₂²	1	2	yes	—
19	C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂²⋊Dic₁₃	C₂²	1	2	yes	—
21	C₂²⋊Dic₁₃	C₂²	1	2	yes	—
22	C₄⋊Dic₁₃	C₂²	1	2	yes	—
23	C₄⋊Dic₁₃	C₂²	1	2	yes	—
24	#6101	C₂²	1	2	yes	—
25	#6101	C₂²	1	2	yes	—
26	#6101	C₂²	1	2	yes	—
27	#6101	C₂²	1	2	yes	—
28	#6101	C₂²	1	2	yes	—
29	C₄×Dic₁₃	C₂²	1	2	yes	—
30	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
31	C₂³×C₁₃	C₂³	1	1	yes	characteristic
32	C₂³×C₁₃	C₂³	1	1	yes	characteristic
33	D₄×C₁₃	—	4	1	no	—
34	C₂×C₄×C₁₃	—	4	1	no	—
35	C₂×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂×Dic₁₃	—	4	1	no	—
39	C₂×Dic₁₃	C₂³	1	2	yes	—
40	C₂×Dic₁₃	C₂³	1	2	yes	—
41	C₂×Dic₁₃	C₂³	1	2	yes	—
42	C₂×Dic₁₃	C₂³	1	2	yes	—
43	Dic₂₆	—	4	1	no	—
44	Dic₂₆	—	4	2	no	—
45	#563	—	13	1	no	maximal, Sylow
46	C₂²×C₁₃	—	2	1	no	—
47	C₂²×C₁₃	—	2	1	no	—
48	C₂²×C₁₃	—	2	2	no	—
49	C₂²×C₁₃	—	2	2	no	—
50	C₂²×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₄×C₁₃	—	2	2	no	—
52	C₄×C₁₃	—	2	1	no	—
53	C₄×C₁₃	—	2	2	no	—
54	Dic₁₃	—	2	2	no	—
55	Dic₁₃	—	2	2	no	—
56	Dic₁₃	—	2	2	no	—
57	Dic₁₃	—	2	2	no	—
58	C₄⋊Q₈	—	13	2	no	—
59	#126	—	13	2	no	—
60	#126	—	13	2	no	—
61	#125	—	13	2	no	—
62	#124	—	13	1	no	—
63	#123	—	13	1	no	—
64	#123	D₁₃	1	1	yes	characteristic
65	C₂²⋊Q₈	—	13	2	no	—
66	C₂²⋊Q₈	—	13	2	no	—
67	C₂×C₁₃	—	4	1	no	—
68	C₂×C₁₃	—	4	1	no	—
69	C₂×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
70	C₂×C₁₃	2₋¹⁺⁴	1	2	yes	—
71	C₂×Q₈	—	13	2	no	—
72	C₂×Q₈	—	13	1	no	—
73	C₂×D₄	C₂×D₁₃	1	1	yes	characteristic
74	C₂²×C₄	—	13	1	no	—
75	C₂²×C₄	C₂×D₁₃	1	1	yes	characteristic
76	C₄⋊C₄	—	13	2	no	—
77	C₄⋊C₄	—	13	2	no	—
78	C₄⋊C₄	—	13	2	no	—
79	C₄⋊C₄	—	13	2	no	—
80	C₄⋊C₄	—	13	2	no	—
81	C₄⋊C₄	—	13	2	no	—
82	C₄⋊C₄	—	13	2	no	—
83	C₄⋊C₄	C₂×D₁₃	1	2	yes	—
84	C₂²⋊C₄	—	13	2	no	—
85	C₂²⋊C₄	—	13	2	no	—
86	C₂²⋊C₄	—	13	2	no	—
87	C₂²⋊C₄	—	13	1	no	—
88	C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
89	C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
90	C₄²	—	13	1	no	—
91	C₄²	—	13	2	no	—
92	C₁₃	#563	1	1	yes	characteristic, complemented, Sylow
93	C₂³	C₂²×D₁₃	1	1	yes	characteristic
94	C₂³	C₂²×D₁₃	1	1	yes	characteristic
95	Q₈	—	52	2	no	—
96	Q₈	—	52	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	13	2	no	—
100	C₂×C₄	—	13	2	no	—
101	C₂×C₄	—	13	2	no	—
102	C₂×C₄	—	13	2	no	—
103	C₂×C₄	—	52	1	no	—
104	C₂×C₄	C₂²×D₁₃	1	2	yes	—
105	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
106	C₂×C₄	C₂²×D₁₃	1	2	yes	—
107	C₂²	—	2	1	no	—
108	C₂²	—	2	1	no	—
109	C₂²	—	2	2	no	—
110	C₂²	—	2	2	no	—
111	C₂²	C₂³×D₁₃	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	2	no	—
115	C₄	—	26	2	no	—
116	C₄	—	26	2	no	—
117	C₄	—	26	2	no	—
118	C₄	—	26	2	no	—
119	C₂	—	4	1	no	—
120	C₂	—	4	1	no	—
121	C₂	#88251	1	1	yes	characteristic
122	C₂	#88257	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#123

C₂

yes

maximal, characteristic

#88190

C₂

yes

maximal, characteristic

#88189

C₂

yes

maximal, characteristic

#88178

C₂

yes

maximal, complemented

#88143

C₂

yes

maximal, complemented

#88142

C₂

yes

maximal, complemented

#88133

C₂

yes

maximal, complemented

#88133

C₂

yes

maximal, complemented

#88132

C₂

yes

maximal, complemented

C₂×D₄×C₁₃

C₂²

yes

characteristic

C₂²×C₄×C₁₃

C₂²

yes

characteristic

C₂²×Dic₁₃

C₂²

yes

characteristic

C₂×Dic₂₆

C₂²

yes

—

C₂×Dic₂₆

C₂²

yes

characteristic

C₁₃×C₄⋊C₄

C₂²

yes

—

C₁₃×C₂²⋊C₄

C₂²

yes

—

C₁₃×C₂²⋊C₄

C₂²

yes

characteristic

C₂²⋊Dic₁₃

C₂²

yes

—

C₂²⋊Dic₁₃

C₂²

yes

characteristic

C₂²⋊Dic₁₃

C₂²

yes

—

C₂²⋊Dic₁₃

C₂²

yes

—

C₄⋊Dic₁₃

C₂²

yes

—

C₄⋊Dic₁₃

C₂²

yes

—

#6101

C₂²

yes

—

#6101

C₂²

yes

—

#6101

C₂²

yes

—

#6101

C₂²

yes

—

#6101

C₂²

yes

—

C₄×Dic₁₃

C₂²

yes

—

C₄×Dic₁₃

C₂²

yes

characteristic

C₂³×C₁₃

C₂³

yes

characteristic

C₂³×C₁₃

C₂³

yes

characteristic

D₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂³

yes

—

C₂×C₄×C₁₃

C₂³

yes

characteristic

C₂×C₄×C₁₃

C₂³

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂³

yes

—

C₂×Dic₁₃

C₂³

yes

—

C₂×Dic₁₃

C₂³

yes

—

C₂×Dic₁₃

C₂³

yes

—

Dic₂₆

—

Dic₂₆

—

#563

—

maximal, Sylow

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂⁴

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

—

C₄⋊Q₈

—

—

—

—

—

—

D₁₃

yes

characteristic

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

H(5,𝔽₂)

yes

characteristic

C₂×C₁₃

2₋¹⁺⁴

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

C₂×D₁₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×D₁₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₁₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₁₃

yes

—

C₂²⋊C₄

C₂×D₁₃

yes

characteristic

C₄²

—

C₄²

—

C₁₃

#563

yes

characteristic, complemented, Sylow

C₂³

C₂²×D₁₃

yes

characteristic

C₂³

C₂²×D₁₃

yes

characteristic

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂²×D₁₃

yes

—

105

C₂×C₄

C₂²×D₁₃

yes

characteristic

106

C₂×C₄

C₂²×D₁₃

yes

—

107

C₂²

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂³×D₁₃

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₂

—

120

C₂

—

121

C₂

#88251

yes

characteristic

122

C₂

#88257

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁴
Fitting	C₁₃×#123	C₂
prime radical	C₂×D₄×C₁₃	C₂²
hypercenter	#123	D₁₃
hypocenter	C₁₃	#563
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #123

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₃

commutator, socle, cosocle

C₂²×C₁₃

C₂⁴

Fitting

C₁₃×#123

C₂

prime radical

C₂×D₄×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂² ◁ #123

N	H ≅ G/N	type
4. #88178	C₂	semidirect
5. #88143	C₂	semidirect
6. #88142	C₂	semidirect
7. #88133	C₂	semidirect
8. #88133	C₂	semidirect
9. #88132	C₂	semidirect
92. C₁₃	#563	semidirect

H ≅ G/N

type

4. #88178

C₂

semidirect

5. #88143

C₂

semidirect

6. #88142

C₂

semidirect

7. #88133

C₂

semidirect

8. #88133

C₂

semidirect

9. #88132

C₂

semidirect

92. C₁₃

#563

semidirect

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

subgroup	index
C₁₃×#123	2
#88190	2
#88189	2
#88178	2
#88143	2
#88142	2
#88133	2
#88132	2
#563	13

subgroup

index

C₁₃×#123

Subgroups — #11719356

Conjugacy classes of subgroups

Complements

Maximal subgroups