Group #13116412 — subgroups

Subgroups — #13116412

Order 1664.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#11718786	C₂	1	1	yes	maximal, characteristic
2	#11718779	C₂	1	1	yes	maximal, characteristic
3	C₁₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
4	#11718125	C₂	1	2	yes	maximal
5	#11718124	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₁₃×#117	C₂²	1	2	yes	—
8	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#6099	C₂²	1	1	yes	characteristic
10	C₂×#6099	C₂²	1	2	yes	—
11	#88059	—	2	2	no	—
12	#88054	—	2	2	no	—
13	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₂²×Dic₁₃	—	2	1	no	—
15	C₁₃×M₁₆	—	2	2	no	—
16	C₂×C₈×C₁₃	D₄	1	2	yes	—
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₂²⋊C₄	—	2	2	no	—
19	C₄²×C₁₃	—	2	2	no	—
20	C₄×Dic₁₃	—	2	1	no	—
21	C₄×Dic₁₃	Q₈	1	1	yes	characteristic
22	C₄×Dic₁₃	Q₈	1	1	yes	characteristic
23	#6099	—	2	2	no	—
24	#6099	—	2	2	no	—
25	#6099	—	2	2	no	—
26	C₂×#1055	—	2	1	no	—
27	C₂×#1055	—	2	2	no	—
28	#2102	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	#41	1	1	yes	characteristic
30	C₂×C₄×C₁₃	—	4	2	no	—
31	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₁₃	#41	1	2	yes	—
34	C₂×C₄×C₁₃	#41	1	2	yes	—
35	C₂×Dic₁₃	—	2	1	no	—
36	C₂×Dic₁₃	—	2	1	no	—
37	C₂×Dic₁₃	—	4	2	no	—
38	C₈×C₁₃	—	2	2	no	—
39	#1055	—	4	1	no	—
40	#1055	—	4	2	no	—
41	#430	—	13	1	no	—
42	#423	—	13	1	no	—
43	#344	—	13	2	no	—
44	#339	—	13	2	no	—
45	H(3,ℤ/4)	D₁₃	1	1	yes	characteristic
46	C₂²×C₁₃	—	4	1	no	—
47	C₂²×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
48	C₂²×C₁₃	#126	1	2	yes	—
49	C₄×C₁₃	—	8	2	no	—
50	C₄×C₁₃	#123	1	1	yes	characteristic
51	C₄×C₁₃	#124	1	1	yes	characteristic
52	C₄×C₁₃	#125	1	2	yes	—
53	Dic₁₃	—	2	2	no	—
54	Dic₁₃	—	4	1	no	—
55	C₂×M₁₆	—	13	2	no	—
56	C₂×M₁₆	—	13	1	no	—
57	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic
58	#117	C₂×D₁₃	1	2	yes	—
59	C₂×C₄²	—	13	1	no	—
60	#108	—	26	2	no	—
61	C₄⋊C₈	—	26	2	no	—
62	C₂×C₁₃	—	2	1	no	—
63	C₂×C₁₃	—	2	2	no	—
64	C₂×C₁₃	#400	1	1	yes	characteristic
65	C₂²×C₄	—	26	1	no	—
66	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
67	M₁₆	—	2	2	no	—
68	M₁₆	—	26	2	no	—
69	M₁₆	—	26	2	no	—
70	M₁₆	—	26	2	no	—
71	C₂×C₈	—	26	1	no	—
72	C₂×C₈	—	26	2	no	—
73	C₂×C₈	D₅₂	1	2	yes	—
74	C₄⋊C₄	—	2	2	no	—
75	C₂²⋊C₄	—	2	2	no	—
76	C₄²	—	2	2	no	—
77	C₄²	—	13	1	no	—
78	C₄²	—	13	1	no	—
79	C₄²	—	26	1	no	—
80	C₁₃	#2102	1	1	yes	characteristic, complemented, Sylow
81	C₂³	#6129	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	26	1	no	—
84	C₂×C₄	—	26	1	no	—
85	C₂×C₄	—	52	2	no	—
86	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
87	C₂×C₄	#6127	1	2	yes	—
88	C₂×C₄	#6129	1	2	yes	—
89	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	52	2	no	—
92	C₈	—	52	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#88133	1	2	yes	—
95	C₂²	#88151	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	—	26	2	no	—
98	C₄	—	52	1	no	—
99	C₄	#88129	1	1	yes	characteristic
100	C₄	#88140	1	1	yes	characteristic
101	C₄	#88143	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#11718320	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11718786

C₂

yes

maximal, characteristic

#11718779

C₂

yes

maximal, characteristic

C₁₃×H(3,ℤ/4)

C₂

yes

maximal, characteristic

#11718125

C₂

yes

maximal

#11718124

C₂

yes

maximal

C₂×C₁₃×M₁₆

C₂²

yes

characteristic

C₁₃×#117

C₂²

yes

—

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

characteristic

C₂×#6099

C₂²

yes

—

#88059

—

#88054

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

Q₈

yes

characteristic

C₄×Dic₁₃

Q₈

yes

—

—

—

—

—

—

C₂³×C₁₃

yes

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

#41

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

—

—

—

—

—

—

D₁₃

yes

characteristic

C₂²×C₁₃

—

C₂²×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₁₃

#126

yes

—

C₄×C₁₃

—

C₄×C₁₃

yes

C₄×C₁₃

yes

C₄×C₁₃

yes

—

Dic₁₃

—

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

characteristic

#117

C₂×D₁₃

yes

—

C₂×C₄²

—

#108

—

C₄⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

—

C₂×C₁₃

#400

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₅₂

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#2102

yes

characteristic, complemented, Sylow

C₂³

#6129

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₅₂

yes

characteristic

C₂×C₄

#6127

yes

—

C₂×C₄

#6129

yes

—

C₂×C₄

Q₈×D₁₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#88133

yes

—

C₂²

#88151

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#88129

yes

characteristic

100

C₄

#88140

yes

characteristic

101

C₄

#88143

yes

—

102

C₂

—

103

C₂

—

104

C₂

#11718320

yes

characteristic

	subgroup	G/H
center	C₄	#88129
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×H(3,ℤ/4)	C₂
socle	C₂×C₁₃	#400
prime radical	C₂³×C₁₃	#41
hypercenter	H(3,ℤ/4)	D₁₃
hypocenter	C₁₃	#2102
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#88129

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×H(3,ℤ/4)

C₂

C₂×C₁₃

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
80. C₁₃	#2102	semidirect

H ≅ G/N

type

80. C₁₃

#2102

semidirect

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

subgroup	index
#11718786	2
#11718779	2
C₁₃×H(3,ℤ/4)	2
#11718125	2
#11718124	2
#2102	13

subgroup

index

C₁₃×H(3,ℤ/4)

Subgroups — #13116412

Conjugacy classes of subgroups

Complements

Maximal subgroups