Group #13116346 — subgroups

Subgroups — #13116346

Order 1664.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×#88057	C₂	1	1	yes	maximal, characteristic
3	#11718656	C₂	1	2	yes	maximal
4	#11718146	C₂	1	2	yes	maximal
5	#11718144	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×#117	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂×#6099	C₂²	1	2	yes	—
11	C₁₃×C₄⋊C₈	—	2	2	no	—
12	#88057	—	2	2	no	—
13	#88048	—	2	2	no	—
14	#88047	—	2	2	no	—
15	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₃	—	2	2	no	—
17	C₁₃×M₁₆	—	2	2	no	—
18	C₂×C₈×C₁₃	—	2	2	no	—
19	C₂×C₈×C₁₃	—	2	1	no	—
20	C₂×C₈×C₁₃	D₄	1	2	yes	—
21	C₁₃×C₄⋊C₄	D₄	1	2	yes	—
22	C₁₃×C₂²⋊C₄	—	2	1	no	—
23	C₄²×C₁₃	—	2	1	no	—
24	C₄⋊Dic₁₃	—	2	2	no	—
25	C₄⋊Dic₁₃	—	2	2	no	—
26	#6099	—	2	2	no	—
27	#6099	Q₈	1	4	yes	—
28	C₂×#1055	—	2	2	no	—
29	#2090	—	13	1	no	maximal, Sylow
30	C₂³×C₁₃	#41	1	1	yes	characteristic
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₁₃	#41	1	2	yes	—
36	C₂×Dic₁₃	—	4	2	no	—
37	C₂×Dic₁₃	—	8	2	no	—
38	C₈×C₁₃	—	2	2	no	—
39	C₈×C₁₃	—	4	1	no	—
40	#1055	—	2	4	no	—
41	#428	—	13	2	no	—
42	C₂×#106	—	13	1	no	—
43	#424	D₁₃	1	1	yes	characteristic
44	#343	—	13	2	no	—
45	#341	—	13	1	no	—
46	C₂²×C₁₃	—	2	2	no	—
47	C₂²×C₁₃	#121	1	1	yes	characteristic
48	C₂²×C₁₃	#125	1	2	yes	—
49	C₄×C₁₃	—	4	2	no	—
50	C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
51	C₄×C₁₃	#123	1	1	yes	characteristic
52	C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₁₃	—	8	2	no	—
54	C₂×M₁₆	—	13	2	no	—
55	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic
56	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
57	#117	C₂×D₁₃	1	1	yes	characteristic
58	C₂×C₄⋊C₄	—	13	2	no	—
59	#107	—	26	2	no	—
60	#106	—	26	2	no	—
61	#106	—	26	2	no	—
62	C₄⋊C₈	—	2	2	no	—
63	C₂×C₁₃	—	2	2	no	—
64	C₂×C₁₃	#398	1	1	yes	characteristic
65	C₂×C₁₃	#471	1	2	yes	—
66	C₂²×C₄	—	26	2	no	—
67	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	13	4	no	—
70	M₁₆	—	26	2	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	26	2	no	—
74	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
75	C₄⋊C₄	—	26	2	no	—
76	C₄⋊C₄	—	26	2	no	—
77	C₄⋊C₄	D₅₂	1	2	yes	—
78	C₂²⋊C₄	—	2	1	no	—
79	C₄²	—	2	1	no	—
80	C₁₃	#2090	1	1	yes	characteristic, complemented, Sylow
81	C₂³	#6127	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	52	2	no	—
84	C₂×C₄	—	104	2	no	—
85	C₂×C₄	C₂×D₅₂	1	1	yes	characteristic
86	C₂×C₄	#6129	1	2	yes	—
87	C₂×C₄	Q₈×D₁₃	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	4	1	no	—
91	C₈	—	26	4	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#88143	1	2	yes	—
94	C₂²	#88184	1	1	yes	characteristic
95	C₄	—	4	2	no	—
96	C₄	—	104	2	no	—
97	C₄	#88151	1	2	yes	—
98	C₄	#88189	1	1	yes	characteristic
99	C₄	#88198	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#11718644	1	1	yes	characteristic
102	C₂	#11718802	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#424

C₂

yes

maximal, characteristic

C₂×#88057

C₂

yes

maximal, characteristic

#11718656

C₂

yes

maximal

#11718146

C₂

yes

maximal

#11718144

C₂

yes

maximal, characteristic

C₂×C₁₃×M₁₆

C₂²

yes

characteristic

C₂²×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#117

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₃

C₂²

yes

—

C₂×#6099

C₂²

yes

—

C₁₃×C₄⋊C₈

—

#88057

—

#88048

—

#88047

—

C₂²×C₄×C₁₃

C₂³

yes

characteristic

C₂²×Dic₁₃

—

C₁₃×M₁₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

D₄

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6099

—

#6099

Q₈

yes

—

—

—

C₂³×C₁₃

yes

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×Q₈

yes

—

C₂×C₄×C₁₃

#41

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

—

—

—

D₁₃

yes

characteristic

#343

—

#341

—

C₂²×C₁₃

—

C₂²×C₁₃

#121

yes

characteristic

C₂²×C₁₃

#125

yes

—

C₄×C₁₃

—

C₄×C₁₃

C₂²⋊Q₈

yes

—

C₄×C₁₃

#123

yes

characteristic

C₄×C₁₃

C₄⋊Q₈

yes

characteristic

Dic₁₃

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₃

yes

characteristic

C₂²×C₈

C₂×D₁₃

yes

characteristic

#117

C₂×D₁₃

yes

characteristic

C₂×C₄⋊C₄

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

#398

yes

characteristic

C₂×C₁₃

#471

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₅₂

yes

—

C₂²⋊C₄

—

C₄²

—

C₁₃

#2090

yes

characteristic, complemented, Sylow

C₂³

#6127

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

104

—

C₂×C₄

C₂×D₅₂

yes

characteristic

C₂×C₄

#6129

yes

—

C₂×C₄

Q₈×D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

#88143

yes

—

C₂²

#88184

yes

characteristic

C₄

—

C₄

—

104

—

C₄

#88151

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#11718644

yes

characteristic

102

C₂

#11718802

yes

—

	subgroup	G/H
center	C₂²	#88184
commutator, cosocle	C₂²×C₄×C₁₃	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃
Fitting	C₁₃×#424	C₂
socle	C₂²×C₁₃	#121
prime radical	C₂³×C₁₃	#41
hypercenter	#424	D₁₃
hypocenter	C₁₃	#2090
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#88184

commutator, cosocle

C₂²×C₄×C₁₃

C₂³

Frattini

C₂²×C₄

C₂²×D₁₃

Fitting

C₁₃×#424

C₂

C₂²×C₁₃

C₂³×C₁₃

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
80. C₁₃	#2090	semidirect

H ≅ G/N

type

80. C₁₃

#2090

semidirect

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

subgroup	index
C₁₃×#424	2
C₂×#88057	2
#11718656	2
#11718146	2
#11718144	2
#2090	13

subgroup

index

C₁₃×#424

Subgroups — #13116346

Conjugacy classes of subgroups

Complements

Maximal subgroups