Group #13113574 — subgroups

Subgroups — #13113574

Order 1664.

210 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 85 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×#533	C₂	1	1	yes	maximal, characteristic
2	#11718585	C₂	1	2	yes	maximal
3	#11718139	C₂	1	4	yes	maximal, complemented
4	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
5	C₁₃×#125	C₄	1	2	yes	—
6	C₁₃×C₂²⋊Q₈	—	2	2	no	—
7	C₄×Q₈×C₁₃	—	2	2	no	—
8	C₁₃×#117	C₄	1	2	yes	—
9	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#6099	—	2	2	no	—
11	C₄⋊#1055	—	2	2	no	—
12	C₄⋊#1055	C₂²	1	4	yes	—
13	C₂×Q₈×C₁₃	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₃	D₄	1	2	yes	—
16	C₁₃×C₄⋊C₄	—	2	4	no	—
17	C₁₃×C₄⋊C₄	—	2	2	no	—
18	C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
19	C₁₃×C₂²⋊C₄	—	2	2	no	—
20	C₄²×C₁₃	—	2	2	no	—
21	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₃	D₄	1	2	yes	—
23	C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	#6099	—	4	4	no	—
25	C₂×#1055	—	2	4	no	—
26	#1561	—	13	1	no	maximal, Sylow
27	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	Q₈×C₁₃	—	4	2	no	—
29	Q₈×C₁₃	—	4	2	no	—
30	C₂×C₄×C₁₃	—	2	2	no	—
31	C₂×C₄×C₁₃	—	2	2	no	—
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	—	2	4	no	—
34	C₂×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
38	#1055	—	4	4	no	—
39	#533	D₁₃	1	1	yes	characteristic
40	#423	—	13	2	no	—
41	#332	—	13	4	no	—
42	C₂²×C₁₃	—	2	1	no	—
43	C₂²×C₁₃	—	2	2	no	—
44	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₄×C₁₃	—	2	1	no	—
46	C₄×C₁₃	—	2	2	no	—
47	C₄×C₁₃	—	4	4	no	—
48	C₄×C₁₃	#101	1	2	yes	—
49	C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
50	C₄×C₁₃	#137	1	2	yes	—
51	C₂×M₁₆	—	26	2	no	—
52	C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
53	#125	Dic₁₃	1	2	yes	—
54	C₂²⋊Q₈	—	2	2	no	—
55	C₄×Q₈	—	2	2	no	—
56	#117	Dic₁₃	1	2	yes	—
57	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
58	C₄⋊C₈	—	13	4	no	—
59	C₄⋊C₈	—	26	2	no	—
60	C₂×C₁₃	—	4	1	no	—
61	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
62	C₂×C₁₃	#417	1	2	yes	—
63	C₂×Q₈	—	2	2	no	—
64	C₂²×C₄	C₂×Dic₁₃	1	1	yes	characteristic
65	C₂²×C₄	C₂²⋊D₁₃	1	2	yes	—
66	M₁₆	—	52	4	no	—
67	C₂×C₈	—	26	4	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	2	2	no	—
70	C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
71	C₂²⋊C₄	—	2	2	no	—
72	C₄²	—	2	2	no	—
73	C₄²	C₂×Dic₁₃	1	1	yes	characteristic
74	C₄²	C₂²⋊D₁₃	1	2	yes	—
75	C₄²	C₂²×D₁₃	1	1	yes	characteristic
76	C₁₃	#1561	1	1	yes	characteristic, complemented, Sylow
77	C₂³	C₂²⋊Dic₁₃	1	1	yes	characteristic
78	Q₈	—	4	2	no	—
79	Q₈	—	4	2	no	—
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	C₂²⋊Dic₁₃	1	2	yes	—
85	C₂×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
86	C₂×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
87	C₂×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
88	C₈	—	52	4	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	2	2	no	—
91	C₂²	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	2	no	—
94	C₄	—	4	4	no	—
95	C₄	#88076	1	2	yes	—
96	C₄	#88203	1	2	yes	—
97	C₄	#88205	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	C₂×#88076	1	1	yes	characteristic
100	C₂	#11718893	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×#533

C₂

yes

maximal, characteristic

#11718585

C₂

yes

maximal

#11718139

C₂

yes

maximal, complemented

C₁₃×C₄⋊Q₈

C₂²

yes

—

C₁₃×#125

C₄

yes

—

C₁₃×C₂²⋊Q₈

—

C₄×Q₈×C₁₃

—

C₁₃×#117

C₄

yes

—

C₂×C₄²×C₁₃

C₂²

yes

—

—

C₂²

yes

—

C₂×Q₈×C₁₃

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₃

D₄

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

D₄

yes

—

C₄²×C₁₃

C₂³

yes

—

—

—

C₂³×C₁₃

C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₃

C₂×D₄

yes

—

#1055

—

#533

D₁₃

yes

characteristic

#423

—

#332

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#101

yes

—

C₄×C₁₃

AGL(1,ℤ/8)

yes

—

C₄×C₁₃

#137

yes

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₁₃

yes

—

#125

Dic₁₃

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

Dic₁₃

yes

—

C₂×C₄²

C₂×D₁₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂×C₁₃

—

C₂×C₁₃

C₂×#101

yes

characteristic

C₂×C₁₃

#417

yes

—

C₂×Q₈

—

C₂²×C₄

C₂×Dic₁₃

yes

characteristic

C₂²×C₄

C₂²⋊D₁₃

yes

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₁₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×Dic₁₃

yes

characteristic

C₄²

C₂²⋊D₁₃

yes

—

C₄²

C₂²×D₁₃

yes

characteristic

C₁₃

#1561

yes

characteristic, complemented, Sylow

C₂³

C₂²⋊Dic₁₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₁₃

yes

—

C₂×C₄

C₂²⋊Dic₁₃

yes

characteristic

C₂×C₄

C₂²×Dic₁₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₁₃

yes

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊Dic₁₃

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#88076

yes

—

C₄

#88203

yes

—

C₄

#88205

yes

—

C₂

—

C₂

C₂×#88076

yes

characteristic

100

C₂

#11718893

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₄²	C₂²×D₁₃
Fitting	C₁₃×#533	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₄²×C₁₃	C₂³
hypercenter	#533	D₁₃
hypocenter	C₁₃	#1561
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂²

C₂×C₂²⋊Dic₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₄²

C₂²×D₁₃

Fitting

C₁₃×#533

C₂

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₃

C₂²⋊C₄

cosocle

C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
3. #11718139	C₂	semidirect
76. C₁₃	#1561	semidirect

H ≅ G/N

type

3. #11718139

C₂

semidirect

76. C₁₃

#1561

semidirect

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

subgroup	index
C₁₃×#533	2
#11718585	2
#11718139	2
#1561	13

subgroup

index

C₁₃×#533

#11718585

#11718139

#1561

Subgroups — #13113574

Conjugacy classes of subgroups

Complements

Maximal subgroups