Group #13130762 — subgroups

Subgroups — #13130762

Order 1664.

180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 66 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	#11719053	C₂	1	1	yes	maximal, characteristic
2	#11719052	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#97	C₂	1	1	yes	maximal, characteristic
4	#11718268	C₂	1	4	yes	maximal
5	C₂×#6118	C₂²	1	2	yes	—
6	C₂×#6118	C₂²	1	2	yes	—
7	C₂×C₈×D₁₃	C₂²	1	2	yes	—
8	C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	#88112	—	2	2	no	—
10	C₄⋊#1057	—	2	2	no	—
11	C₁₃×#97	C₄	1	1	yes	characteristic
12	#88055	C₄	1	2	yes	—
13	#88043	C₄	1	1	yes	characteristic
14	C₂×C₄×D₁₃	Q₈	1	2	yes	—
15	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
16	C₂×#1057	—	2	2	no	—
17	C₂×#1057	—	2	2	no	—
18	#6118	—	2	4	no	—
19	#6118	—	2	4	no	—
20	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₃	D₄	1	2	yes	—
24	C₂×#1055	C₂×C₄	1	2	yes	—
25	C₈×D₁₃	—	2	2	no	—
26	C₈×D₁₃	—	2	2	no	—
27	#1838	—	13	1	no	maximal, Sylow
28	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
32	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
33	C₄×D₁₃	—	4	2	no	—
34	C₄×D₁₃	#41	1	2	yes	—
35	C₄×D₁₃	#41	1	2	yes	—
36	#1057	—	4	2	no	—
37	#1057	—	4	2	no	—
38	C₈×C₁₃	—	2	2	no	—
39	#1055	—	2	2	no	—
40	#423	—	13	1	no	—
41	#423	—	13	1	no	—
42	C₂×#97	—	13	1	no	—
43	#341	—	13	4	no	—
44	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂×D₁₃	—	2	2	no	—
46	C₂×D₁₃	#125	1	2	yes	—
47	C₄×C₁₃	—	2	2	no	—
48	C₄×C₁₃	#117	1	2	yes	—
49	Dic₁₃	—	2	2	no	—
50	Dic₁₃	#124	1	1	yes	characteristic
51	Dic₁₃	#124	1	1	yes	characteristic
52	C₂×M₁₆	—	13	2	no	—
53	C₂×M₁₆	—	13	2	no	—
54	C₂²×C₈	—	13	2	no	—
55	C₂×C₄²	—	13	1	no	—
56	C₄⋊C₈	—	26	2	no	—
57	C₄⋊C₈	—	26	2	no	—
58	#97	—	13	2	no	—
59	#97	—	13	1	no	—
60	#97	#261	1	1	yes	characteristic
61	C₂×C₁₃	#382	1	1	yes	characteristic
62	C₂×C₁₃	#430	1	2	yes	—
63	D₁₃	—	2	2	no	—
64	C₂²×C₄	—	13	1	no	—
65	C₂²×C₄	—	13	2	no	—
66	M₁₆	—	26	4	no	—
67	M₁₆	—	26	4	no	—
68	C₂×C₈	—	13	2	no	—
69	C₂×C₈	—	26	2	no	—
70	C₂×C₈	—	26	2	no	—
71	C₂×C₈	—	26	2	no	—
72	C₂×C₈	—	26	2	no	—
73	C₂×C₈	C₂×#261	1	2	yes	—
74	C₄²	—	13	2	no	—
75	C₄²	—	13	1	no	—
76	C₄²	C₂×#261	1	1	yes	characteristic
77	C₁₃	#1838	1	1	yes	characteristic, complemented, Sylow
78	C₂³	—	13	1	no	—
79	C₂×C₄	—	13	1	no	—
80	C₂×C₄	—	13	2	no	—
81	C₂×C₄	—	13	2	no	—
82	C₂×C₄	—	13	2	no	—
83	C₂×C₄	—	52	2	no	—
84	C₂×C₄	C₄⋊#261	1	2	yes	—
85	C₂×C₄	C₂²×#261	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	26	2	no	—
88	C₈	—	52	2	no	—
89	C₈	—	52	2	no	—
90	C₂²	—	13	2	no	—
91	C₂²	—	26	2	no	—
92	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	13	1	no	—
95	C₄	—	13	1	no	—
96	C₄	—	26	2	no	—
97	C₄	#88237	1	2	yes	—
98	C₂	—	26	2	no	—
99	C₂	#11719060	1	1	yes	characteristic
100	C₂	#11719100	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719053

C₂

yes

maximal, characteristic

#11719052

C₂

yes

maximal, characteristic

D₁₃×#97

C₂

yes

maximal, characteristic

#11718268

C₂

yes

maximal

C₂×#6118

C₂²

yes

—

C₂×#6118

C₂²

yes

—

C₂×C₈×D₁₃

C₂²

yes

—

C₄²×D₁₃

C₂²

yes

characteristic

#88112

—

C₄⋊#1057

—

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

—

#88043

C₄

yes

characteristic

C₂×C₄×D₁₃

Q₈

yes

—

C₂×C₄×D₁₃

C₂³

yes

—

—

—

—

C₂×C₈×C₁₃

C₂×C₄

yes

—

C₄²×C₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

C₂×#1055

C₂×C₄

yes

—

C₈×D₁₃

—

C₈×D₁₃

—

#1838

—

maximal, Sylow

C₂²×D₁₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

#41

yes

—

C₄×D₁₃

#41

yes

—

#1057

—

#1057

—

C₈×C₁₃

—

#1055

—

#423

—

#423

—

C₂×#97

—

#341

—

C₂²×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

#125

yes

—

C₄×C₁₃

—

C₄×C₁₃

#117

yes

—

Dic₁₃

—

Dic₁₃

yes

Dic₁₃

yes

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂×C₁₃

yes

C₂×C₁₃

yes

—

D₁₃

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#261

yes

—

C₄²

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₃

#1838

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊#261

yes

—

C₂×C₄

C₂²×#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₄⋊#261

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#88237

yes

—

C₂

—

C₂

#11719060

yes

characteristic

100

C₂

#11719100

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#97	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#1838
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#97

C₄

socle

C₂²×C₁₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₃

C₂×Q₈

cosocle

C₂×C₄×D₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
77. C₁₃	#1838	semidirect

H ≅ G/N

type

77. C₁₃

#1838

semidirect

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

subgroup	index
#11719053	2
#11719052	2
D₁₃×#97	2
#11718268	2
#1838	13

subgroup

index

D₁₃×#97

Subgroups — #13130762

Conjugacy classes of subgroups

Complements

Maximal subgroups