Group #13114503 — subgroups

Subgroups — #13114503

Order 1664.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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×#493	C₂	1	1	yes	maximal, characteristic, complemented
2	#11718734	C₂	1	2	yes	maximal, complemented
3	#11718731	C₂	1	2	yes	maximal, complemented
4	#11718354	C₂	1	1	yes	maximal, characteristic, complemented
5	#11718047	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₈	—	2	2	no	—
7	C₁₃×#127	C₂²	1	2	yes	—
8	C₂×#6104	—	2	4	no	—
9	C₂×#6095	—	2	2	no	—
10	#88128	C₂²	1	1	yes	characteristic
11	#88123	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	#88072	—	2	4	no	—
14	C₄×#1055	C₂²	1	2	yes	—
15	C₂×D₄×C₁₃	—	2	2	no	—
16	C₂×D₄×C₁₃	—	2	2	no	—
17	C₂×D₄×C₁₃	—	2	2	no	—
18	C₂×D₅₂	—	2	1	no	—
19	C₂×D₅₂	—	2	2	no	—
20	C₂×Dic₂₆	—	2	1	no	—
21	C₁₃×D₈	—	4	4	no	—
22	C₂×C₈×C₁₃	D₄	1	2	yes	—
23	C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	#6104	—	4	8	no	—
25	C₄⋊Dic₁₃	—	2	2	no	—
26	C₂×#1055	D₄	1	4	yes	—
27	#6095	—	4	4	no	—
28	#1721	—	13	1	no	maximal, Sylow
29	C₂³×C₁₃	—	4	2	no	—
30	C₂²×D₁₃	—	4	1	no	—
31	D₄×C₁₃	—	4	4	no	—
32	D₄×C₁₃	—	4	4	no	—
33	D₄×C₁₃	—	4	4	no	—
34	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
36	C₂×Dic₁₃	—	4	1	no	—
37	D₅₂	—	4	2	no	—
38	D₅₂	—	4	4	no	—
39	Dic₂₆	—	4	2	no	—
40	C₈×C₁₃	D₈	1	4	yes	complemented
41	#1055	—	2	4	no	—
42	#493	—	13	2	no	—
43	#493	D₁₃	1	1	yes	characteristic, complemented
44	#492	—	13	1	no	—
45	#486	—	13	2	no	—
46	#322	—	13	1	no	—
47	C₂²×C₁₃	—	8	2	no	—
48	C₂²×C₁₃	—	8	2	no	—
49	C₂²×C₁₃	—	8	2	no	—
50	C₂²×C₁₃	#127	1	1	yes	characteristic
51	C₂×D₁₃	—	8	1	no	—
52	C₂×D₁₃	—	8	2	no	—
53	C₄×C₁₃	C₂×D₈	1	2	yes	—
54	C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
55	Dic₁₃	—	8	1	no	—
56	C₂×SD₁₆	—	26	2	no	—
57	C₂×D₈	—	2	2	no	—
58	C₂×D₈	—	26	4	no	—
59	C₄⋊Q₈	—	13	1	no	—
60	#127	—	13	1	no	—
61	#127	C₂×D₁₃	1	2	yes	—
62	#102	—	26	4	no	—
63	C₄×C₈	—	13	2	no	—
64	C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
65	C₂×C₁₃	—	16	2	no	—
66	C₂×C₁₃	#493	1	1	yes	characteristic
67	C₂×C₁₃	#496	1	2	yes	—
68	D₁₃	—	16	1	no	—
69	C₂×Q₈	—	26	1	no	—
70	C₂×D₄	—	2	2	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	2	no	—
73	C₂×D₄	—	26	2	no	—
74	C₂×D₄	—	26	1	no	—
75	SD₁₆	—	52	4	no	—
76	D₈	—	4	4	no	—
77	D₈	—	52	8	no	—
78	C₂×C₈	—	13	4	no	—
79	C₂×C₈	C₂²⋊D₁₃	1	2	yes	—
80	C₄⋊C₄	—	26	2	no	—
81	C₄²	C₂²×D₁₃	1	1	yes	characteristic
82	C₁₃	#1721	1	1	yes	characteristic, complemented, Sylow
83	C₂³	—	4	2	no	—
84	C₂³	—	52	1	no	—
85	Q₈	—	52	2	no	—
86	D₄	—	4	4	no	—
87	D₄	—	4	4	no	—
88	D₄	—	4	4	no	—
89	D₄	—	52	4	no	—
90	D₄	—	52	2	no	—
91	C₂×C₄	—	52	1	no	—
92	C₂×C₄	D₄×D₁₃	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
94	C₈	—	26	4	no	—
95	C₈	#6104	1	4	yes	complemented
96	C₂²	—	8	2	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	8	2	no	—
99	C₂²	—	104	1	no	—
100	C₂²	—	104	2	no	—
101	C₂²	#88194	1	1	yes	characteristic
102	C₄	—	104	1	no	—
103	C₄	#88165	1	4	yes	—
104	C₄	C₂×#6104	1	2	yes	—
105	C₂	—	16	2	no	—
106	C₂	—	208	1	no	—
107	C₂	#11718734	1	1	yes	characteristic
108	C₂	#11718815	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#493

C₂

yes

maximal, characteristic, complemented

#11718734

C₂

yes

maximal, complemented

#11718731

C₂

yes

maximal, complemented

#11718354

C₂

yes

maximal, characteristic, complemented

#11718047

C₂

yes

maximal, characteristic, complemented

C₂×C₁₃×D₈

—

C₁₃×#127

C₂²

yes

—

C₂×#6104

—

C₂×#6095

—

#88128

C₂²

yes

characteristic

#88123

C₂²

yes

characteristic

C₄×C₈×C₁₃

C₂²

yes

characteristic

#88072

—

C₄×#1055

C₂²

yes

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×Dic₂₆

—

C₁₃×D₈

—

C₂×C₈×C₁₃

D₄

yes

—

C₄²×C₁₃

C₂³

yes

characteristic

#6104

—

C₄⋊Dic₁₃

—

C₂×#1055

D₄

yes

—

#6095

—

#1721

—

maximal, Sylow

C₂³×C₁₃

—

C₂²×D₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

C₂×Dic₁₃

—

D₅₂

—

D₅₂

—

Dic₂₆

—

C₈×C₁₃

D₈

yes

—

—

D₁₃

yes

characteristic, complemented

#492

—

#486

—

#322

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

#127

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

C₂×D₈

yes

—

C₄×C₁₃

AGL(1,ℤ/8)

yes

—

Dic₁₃

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

#127

C₂×D₁₃

yes

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₁₃

yes

characteristic

C₂×C₁₃

—

C₂×C₁₃

#493

yes

characteristic

C₂×C₁₃

#496

yes

—

D₁₃

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₃

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₁₃

yes

characteristic

C₁₃

#1721

yes

characteristic, complemented, Sylow

C₂³

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₃

yes

—

C₂×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

C₈

—

C₈

#6104

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

104

—

100

C₂²

—

104

—

101

C₂²

#88194

yes

characteristic

102

C₄

—

104

—

103

C₄

#88165

yes

—

104

C₄

C₂×#6104

yes

—

105

C₂

—

106

C₂

—

208

—

107

C₂

#11718734

yes

characteristic

108

C₂

#11718815

yes

—

	subgroup	G/H
center	C₂²	#88194
commutator, cosocle	C₄²×C₁₃	C₂³
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#493	C₂
socle	C₂²×C₁₃	#127
hypercenter	#493	D₁₃
hypocenter	C₁₃	#1721
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

subgroup

G/H

center

C₂²

#88194

commutator, cosocle

C₄²×C₁₃

C₂³

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#493

C₂

C₂²×C₁₃

D₁₃

C₁₃

G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #493

N	H ≅ G/N	type
1. C₁₃×#493	C₂	semidirect
2. #11718734	C₂	semidirect
3. #11718731	C₂	semidirect
4. #11718354	C₂	semidirect
5. #11718047	C₂	semidirect
40. C₈×C₁₃	D₈	semidirect
43. #493	D₁₃	semidirect
82. C₁₃	#1721	semidirect
95. C₈	#6104	semidirect

H ≅ G/N

type

1. C₁₃×#493

C₂

semidirect

2. #11718734

C₂

semidirect

3. #11718731

C₂

semidirect

4. #11718354

C₂

semidirect

5. #11718047

C₂

semidirect

40. C₈×C₁₃

D₈

semidirect

43. #493

D₁₃

semidirect

82. C₁₃

#1721

semidirect

95. C₈

#6104

semidirect

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

subgroup	index
C₁₃×#493	2
#11718734	2
#11718731	2
#11718354	2
#11718047	2
#1721	13

subgroup

index

C₁₃×#493

Subgroups — #13114503

Conjugacy classes of subgroups

Complements

Maximal subgroups