Group #13131172 — subgroups

Subgroups — #13131172

Order 1664.

160 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 76 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×#88098	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#11718369	C₂	1	1	yes	maximal, characteristic
4	#11718260	C₂	1	2	yes	maximal, complemented
5	C₄⋊#6092	C₂	1	2	yes	maximal, complemented
6	C₂×#6094	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	#88126	C₄	1	1	yes	characteristic
9	C₂×#6092	C₂²	1	2	yes	—
10	C₂×#6092	C₂²	1	2	yes	—
11	#88098	—	2	2	no	—
12	D₁₃⋊C₁₆	—	2	2	no	—
13	C₁₃×#97	C₄	1	1	yes	characteristic
14	#88055	C₄	1	1	yes	characteristic
15	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₄×#1055	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	#6103	C₈	1	2	yes	—
22	#6101	C₈	1	2	yes	—
23	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#1055	C₂×C₄	1	1	yes	characteristic
25	C₂×#1055	C₂³	1	1	yes	characteristic
26	#6094	—	2	2	no	—
27	C₈×D₁₃	D₄	1	2	yes	—
28	C₈×D₁₃	Q₈	1	2	yes	—
29	#6092	—	2	2	no	—
30	#6092	—	2	2	no	—
31	#2151	—	13	1	no	maximal, Sylow
32	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₁₃	C₂×C₈	1	2	yes	—
36	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
37	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
38	C₄×D₁₃	M₁₆	1	2	yes	—
39	C₈×C₁₃	—	2	1	no	—
40	C₈×C₁₃	C₄⋊C₄	1	2	yes	—
41	#1055	—	2	1	no	—
42	#1055	C₂×D₄	1	1	yes	characteristic
43	#1055	C₂×Q₈	1	1	yes	characteristic
44	C₂×M₃₂	—	13	1	no	—
45	C₂²×C₁₆	—	13	1	no	—
46	#405	—	13	1	no	—
47	C₄⋊C₁₆	—	13	2	no	—
48	C₄⋊C₁₆	—	13	2	no	—
49	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
50	C₂×D₁₃	—	2	2	no	—
51	C₂×D₁₃	C₄⋊C₈	1	2	yes	—
52	C₄×C₁₃	—	2	2	no	—
53	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
55	Dic₁₃	—	2	2	no	—
56	Dic₁₃	C₄⋊C₈	1	2	yes	—
57	C₂×M₁₆	—	13	1	no	—
58	C₂²×C₈	—	13	1	no	—
59	#117	—	13	1	no	—
60	M₃₂	—	26	2	no	—
61	C₂×C₁₆	—	13	2	no	—
62	C₂×C₁₆	—	13	2	no	—
63	C₂×C₁₆	—	26	2	no	—
64	#97	—	13	1	no	—
65	#97	#261	1	1	yes	characteristic
66	C₄×C₈	—	13	1	no	—
67	C₄×C₈	—	13	1	no	—
68	C₂×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₁₃	#504	1	2	yes	—
70	D₁₃	—	2	2	no	—
71	C₂²×C₄	—	13	1	no	—
72	M₁₆	—	26	2	no	—
73	C₂×C₈	—	13	1	no	—
74	C₂×C₈	—	13	2	no	—
75	C₂×C₈	—	13	2	no	—
76	C₂×C₈	—	13	1	no	—
77	C₂×C₈	C₂×#261	1	1	yes	characteristic
78	C₂×C₈	C₂×#261	1	1	yes	characteristic
79	C₄⋊C₄	—	13	2	no	—
80	C₂²⋊C₄	—	13	2	no	—
81	C₄²	—	13	1	no	—
82	C₄²	C₂×#261	1	1	yes	characteristic
83	C₁₆	—	26	2	no	—
84	C₁₆	—	26	2	no	—
85	C₁₃	#2151	1	1	yes	characteristic, complemented, Sylow
86	C₂³	—	13	1	no	—
87	C₂×C₄	—	13	1	no	—
88	C₂×C₄	—	13	2	no	—
89	C₂×C₄	—	13	2	no	—
90	C₂×C₄	—	13	2	no	—
91	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
92	C₂×C₄	C₂²×#261	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	13	1	no	—
95	C₈	—	13	1	no	—
96	C₈	—	26	1	no	—
97	C₈	C₄⋊#261	1	2	yes	—
98	C₂²	—	13	2	no	—
99	C₂²	—	26	2	no	—
100	C₂²	C₂×D₁₃⋊C₈	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	13	2	no	—
103	C₄	—	26	2	no	—
104	C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
105	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
106	C₂	—	26	2	no	—
107	C₂	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
108	C₂	#11719096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#88098

C₂

yes

maximal, characteristic

C₂×D₁₃⋊C₁₆

C₂

yes

maximal, characteristic

#11718369

C₂

yes

maximal, characteristic

#11718260

C₂

yes

maximal, complemented

C₄⋊#6092

C₂

yes

maximal, complemented

C₂×#6094

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

#88126

C₄

yes

characteristic

C₂×#6092

C₂²

yes

—

C₂×#6092

C₂²

yes

—

#88098

—

D₁₃⋊C₁₆

—

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₄×#1055

C₂²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

#6103

C₈

yes

—

#6101

C₈

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂³

yes

characteristic

#6094

—

C₈×D₁₃

D₄

yes

—

C₈×D₁₃

Q₈

yes

—

—

—

—

C₂²×D₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

C₄⋊C₄

yes

—

C₄×D₁₃

M₁₆

yes

—

C₈×C₁₃

—

C₈×C₁₃

C₄⋊C₄

yes

—

#1055

—

#1055

C₂×D₄

yes

characteristic

#1055

C₂×Q₈

yes

characteristic

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

C₄⋊C₈

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₃

C₂×M₁₆

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄⋊C₈

yes

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₃

#504

yes

—

D₁₃

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₆

—

C₁₆

—

C₁₃

#2151

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₃⋊C₈

yes

—

C₂×C₄

C₂²×#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₄⋊#261

yes

—

C₂²

—

C₂²

—

100

C₂²

C₂×D₁₃⋊C₈

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

D₁₃⋊M₁₆

yes

characteristic

105

C₄

C₂×C₄⋊#261

yes

characteristic

106

C₂

—

107

C₂

D₁₃⋊(C₄⋊C₈)

yes

characteristic

108

C₂

#11719096

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×#97	C₄
prime radical	C₂²×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#2151
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂²×C₈

Fitting

C₁₃×#97

C₄

prime radical

C₂²×D₁₃

C₂×C₈

C₂³

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
4. #11718260	C₂	semidirect
5. C₄⋊#6092	C₂	semidirect
85. C₁₃	#2151	semidirect

H ≅ G/N

type

4. #11718260

C₂

semidirect

5. C₄⋊#6092

C₂

semidirect

85. C₁₃

#2151

semidirect

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

subgroup	index
C₂×#88098	2
C₂×D₁₃⋊C₁₆	2
#11718369	2
#11718260	2
C₄⋊#6092	2
#2151	13

subgroup

index

C₂×D₁₃⋊C₁₆

Subgroups — #13131172

Conjugacy classes of subgroups

Complements

Maximal subgroups