Group #13130341 — subgroups

Subgroups — #13130341

Order 1664.

202 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 62 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	#11719222	C₂	1	1	yes	maximal, characteristic
2	#11719125	C₂	1	2	yes	maximal
3	#11718245	C₂	1	4	yes	maximal, complemented
4	C₁₃×#117	C₄	1	1	yes	characteristic
5	#88180	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
7	#88144	C₄	1	2	yes	—
8	#88142	C₂²	1	2	yes	—
9	#88132	—	2	2	no	—
10	C₄×Dic₂₆	—	2	2	no	—
11	C₂²⋊#1057	—	2	2	no	—
12	#88112	C₂²	1	4	yes	—
13	C₄×#1057	—	2	2	no	—
14	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₁₃	D₄	1	2	yes	—
16	C₂×Dic₂₆	—	2	2	no	—
17	C₂×#1057	—	2	4	no	—
18	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
19	C₁₃×C₂²⋊C₄	—	2	1	no	—
20	C₄²×C₁₃	—	2	1	no	—
21	C₂²⋊Dic₁₃	—	2	1	no	—
22	C₄⋊Dic₁₃	—	2	2	no	—
23	C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
24	#6101	—	2	2	no	—
25	#6101	—	2	2	no	—
26	C₄×Dic₁₃	—	2	1	no	—
27	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₁₃	D₄	1	2	yes	—
29	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
30	#1544	—	13	1	no	maximal, Sylow
31	C₂³×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃	—	2	2	no	—
33	C₂×C₄×C₁₃	—	2	2	no	—
34	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₁₃	—	2	4	no	—
37	C₂×Dic₁₃	—	2	2	no	—
38	C₂×Dic₁₃	C₂²⋊C₄	1	2	yes	—
39	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
40	Dic₂₆	—	4	4	no	—
41	#1057	—	4	4	no	—
42	#533	—	13	1	no	—
43	#431	—	13	2	no	—
44	#332	—	13	4	no	—
45	C₂²×C₁₃	—	2	1	no	—
46	C₂²×C₁₃	—	2	2	no	—
47	C₂²×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₄×C₁₃	—	2	1	no	—
49	C₄×C₁₃	—	4	2	no	—
50	C₄×C₁₃	#101	1	2	yes	—
51	Dic₁₃	—	2	2	no	—
52	Dic₁₃	—	4	2	no	—
53	Dic₁₃	#135	1	4	yes	—
54	C₄⋊Q₈	—	13	2	no	—
55	#125	—	13	2	no	—
56	C₂²⋊Q₈	—	26	2	no	—
57	C₄×Q₈	—	26	2	no	—
58	#117	—	13	1	no	—
59	#117	#261	1	1	yes	characteristic
60	C₂×C₄²	—	13	1	no	—
61	C₄⋊C₈	—	13	4	no	—
62	C₂²⋊C₈	—	26	2	no	—
63	C₄×C₈	—	26	2	no	—
64	C₂×C₁₃	—	4	1	no	—
65	C₂×C₁₃	C₂×#101	1	1	yes	characteristic
66	C₂×C₁₃	#416	1	2	yes	—
67	C₂×Q₈	—	26	2	no	—
68	C₂²×C₄	—	13	2	no	—
69	C₂²×C₄	C₂×#261	1	1	yes	characteristic
70	C₂×C₈	—	26	4	no	—
71	C₄⋊C₄	—	13	2	no	—
72	C₄⋊C₄	—	26	2	no	—
73	C₄⋊C₄	—	26	2	no	—
74	C₄⋊C₄	—	26	2	no	—
75	C₄⋊C₄	C₂×#261	1	2	yes	—
76	C₂²⋊C₄	—	2	1	no	—
77	C₂²⋊C₄	—	26	1	no	—
78	C₄²	—	2	1	no	—
79	C₄²	—	13	2	no	—
80	C₄²	—	13	1	no	—
81	C₄²	—	13	1	no	—
82	C₄²	—	26	1	no	—
83	C₁₃	#1544	1	1	yes	characteristic, complemented, Sylow
84	C₂³	C₂²⋊#261	1	1	yes	characteristic
85	Q₈	—	52	4	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	13	2	no	—
89	C₂×C₄	—	13	2	no	—
90	C₂×C₄	—	26	4	no	—
91	C₂×C₄	—	26	2	no	—
92	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
93	C₂×C₄	C₂²×#261	1	1	yes	characteristic
94	C₈	—	52	4	no	—
95	C₂²	—	2	1	no	—
96	C₂²	—	2	2	no	—
97	C₂²	C₂×C₂²⋊#261	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	4	2	no	—
100	C₄	—	13	4	no	—
101	C₄	—	26	2	no	—
102	C₄	—	52	2	no	—
103	C₄	#88113	1	2	yes	—
104	C₂	—	4	1	no	—
105	C₂	C₂×#88113	1	1	yes	characteristic
106	C₂	#11719165	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11719222

C₂

yes

maximal, characteristic

#11719125

C₂

yes

maximal

#11718245

C₂

yes

maximal, complemented

C₁₃×#117

C₄

yes

characteristic

#88180

C₄

yes

characteristic

C₂×C₄×Dic₁₃

C₂²

yes

characteristic

#88144

C₄

yes

—

#88142

C₂²

yes

—

#88132

—

C₄×Dic₂₆

—

C₂²⋊#1057

—

#88112

C₂²

yes

—

C₄×#1057

—

C₂²×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂²×Dic₁₃

D₄

yes

—

C₂×Dic₂₆

—

C₂×#1057

—

C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

C₂×C₄

yes

—

#6101

—

#6101

—

C₄×Dic₁₃

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₄×Dic₁₃

D₄

yes

—

C₄×Dic₁₃

C₂³

yes

characteristic

#1544

—

maximal, Sylow

C₂³×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂²⋊C₄

yes

—

C₂×Dic₁₃

C₂×D₄

yes

—

Dic₂₆

—

—

—

—

—

C₂²×C₁₃

—

C₂²×C₁₃

—

C₂²×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#101

yes

—

Dic₁₃

—

Dic₁₃

—

Dic₁₃

#135

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

—

yes

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₂×C₁₃

—

C₂×C₁₃

C₂×#101

yes

characteristic

C₂×C₁₃

#416

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×#261

yes

characteristic

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×#261

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₁₃

#1544

yes

characteristic, complemented, Sylow

C₂³

C₂²⋊#261

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#261

yes

characteristic

C₂×C₄

C₂²×#261

yes

characteristic

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₂²⋊#261

yes

characteristic

C₄

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#88113

yes

—

104

C₂

—

105

C₂

C₂×#88113

yes

characteristic

106

C₂

#11719165

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×#117	C₄
socle	C₂²×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂³×C₁₃	C₂²⋊C₄
cosocle	C₄×Dic₁₃	C₂³
hypercenter	#117	#261
hypocenter	C₁₃	#1544
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

subgroup

G/H

center

C₂×C₄

C₂²⋊#261

commutator

C₂×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#261

Fitting

C₁₃×#117

C₄

socle

C₂²×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂³×C₁₃

C₂²⋊C₄

cosocle

C₄×Dic₁₃

C₂³

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

N	H ≅ G/N	type
3. #11718245	C₂	semidirect
83. C₁₃	#1544	semidirect

H ≅ G/N

type

3. #11718245

C₂

semidirect

83. C₁₃

#1544

semidirect

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

subgroup	index
#11719222	2
#11719125	2
#11718245	2
#1544	13

subgroup

index

Subgroups — #13130341

Conjugacy classes of subgroups

Complements

Maximal subgroups