Group #13131203 — subgroups

Subgroups — #13131203

Order 1664.

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

normal subgroups only

This group has 138 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	#11718369	C₂	1	1	yes	maximal, characteristic
2	#11718260	C₂	1	2	yes	maximal, complemented
3	#11718259	C₂	1	2	yes	maximal
4	#11718231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#6094	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	#88126	C₄	1	1	yes	characteristic
9	C₂×#6092	C₂²	1	2	yes	—
10	C₂×#6092	C₂²	1	2	yes	—
11	C₁₃×#97	C₄	1	1	yes	characteristic
12	#88055	C₄	1	1	yes	characteristic
13	C₈×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₄×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	#6103	C₈	1	2	yes	—
20	#6101	C₈	1	2	yes	—
21	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂×#1055	C₂³	1	1	yes	characteristic
24	#6094	—	2	2	no	—
25	C₈×D₁₃	—	2	2	no	—
26	#6092	—	2	2	no	—
27	#6092	—	2	2	no	—
28	#2164	—	13	1	no	maximal, Sylow
29	C₂²×D₁₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₁₃	C₂×C₈	1	2	yes	—
33	C₂×Dic₁₃	C₂×C₈	1	1	yes	characteristic
34	C₄×D₁₃	—	2	1	no	—
35	C₄×D₁₃	—	2	1	no	—
36	C₈×C₁₃	—	2	1	no	—
37	C₈×C₁₃	—	2	1	no	—
38	#1055	M₁₆	1	2	yes	—
39	#1055	#41	1	2	yes	—
40	#405	—	13	1	no	—
41	C₄⋊C₁₆	—	13	2	no	—
42	C₂²⋊C₁₆	—	13	2	no	—
43	#346	—	13	1	no	—
44	C₄×C₁₆	—	13	1	no	—
45	C₂²×C₁₃	C₂²×C₈	1	1	yes	characteristic
46	C₂×D₁₃	—	2	1	no	—
47	C₂×D₁₃	—	2	2	no	—
48	C₄×C₁₃	—	2	2	no	—
49	C₄×C₁₃	#117	1	1	yes	characteristic
50	C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
51	Dic₁₃	—	2	1	no	—
52	Dic₁₃	—	2	2	no	—
53	C₂×M₁₆	—	13	1	no	—
54	C₂²×C₈	—	13	1	no	—
55	#117	—	13	1	no	—
56	C₂×C₁₆	—	13	2	no	—
57	C₂×C₁₆	—	13	2	no	—
58	#97	—	13	1	no	—
59	#97	#261	1	1	yes	characteristic
60	C₄×C₈	—	13	1	no	—
61	C₄×C₈	—	13	1	no	—
62	C₂×C₁₃	#431	1	1	yes	characteristic
63	C₂×C₁₃	#504	1	2	yes	—
64	D₁₃	—	4	1	no	—
65	C₂²×C₄	—	13	1	no	—
66	M₁₆	—	26	2	no	—
67	C₂×C₈	—	13	1	no	—
68	C₂×C₈	—	13	1	no	—
69	C₂×C₈	—	26	2	no	—
70	C₂×C₈	C₂×#261	1	1	yes	characteristic
71	C₂×C₈	C₂×#261	1	1	yes	characteristic
72	C₄⋊C₄	—	13	2	no	—
73	C₂²⋊C₄	—	13	2	no	—
74	C₄²	—	13	1	no	—
75	C₄²	C₂×#261	1	1	yes	characteristic
76	C₁₆	—	26	2	no	—
77	C₁₆	—	26	2	no	—
78	C₁₃	#2164	1	1	yes	characteristic, complemented, Sylow
79	C₂³	—	13	1	no	—
80	C₂×C₄	—	13	2	no	—
81	C₂×C₄	—	13	1	no	—
82	C₂×C₄	—	26	1	no	—
83	C₂×C₄	—	26	1	no	—
84	C₂×C₄	D₁₃⋊C₈	1	2	yes	—
85	C₂×C₄	C₂²×#261	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	—	13	2	no	—
89	C₈	—	13	2	no	—
90	C₂²	—	26	1	no	—
91	C₂²	—	26	2	no	—
92	C₂²	C₂×D₁₃⋊C₈	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	26	1	no	—
95	C₄	—	26	2	no	—
96	C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
97	C₄	#88237	1	1	yes	characteristic
98	C₂	—	52	1	no	—
99	C₂	#11719049	1	1	yes	characteristic
100	C₂	#11719096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11718369

C₂

yes

maximal, characteristic

#11718260

C₂

yes

maximal, complemented

#11718259

C₂

yes

maximal

#11718231

C₂

yes

maximal, characteristic, complemented

C₄×#6092

C₂

yes

maximal, characteristic, complemented

C₂×#6094

C₄

yes

characteristic

C₂×C₈×D₁₃

C₂²

yes

characteristic

#88126

C₄

yes

characteristic

C₂×#6092

C₂²

yes

—

C₂×#6092

C₂²

yes

—

C₁₃×#97

C₄

yes

characteristic

#88055

C₄

yes

characteristic

C₈×Dic₁₃

C₂²

yes

characteristic

C₄×#1055

C₂²

yes

characteristic

C₂×C₄×D₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄²×C₁₃

C₂×C₄

yes

characteristic

#6103

C₈

yes

—

#6101

C₈

yes

—

C₄×Dic₁₃

C₂×C₄

yes

characteristic

C₂×#1055

C₂×C₄

yes

characteristic

C₂×#1055

C₂³

yes

characteristic

#6094

—

C₈×D₁₃

—

—

—

—

C₂²×D₁₃

C₂×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₈

yes

—

C₂×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₃

C₂×C₈

yes

—

C₂×Dic₁₃

C₂×C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

#1055

M₁₆

yes

—

#1055

#41

yes

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

—

C₂²×C₁₃

C₂²×C₈

yes

characteristic

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

#117

yes

characteristic

C₄×C₁₃

C₂×M₁₆

yes

characteristic

Dic₁₃

—

Dic₁₃

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂×C₁₃

#431

yes

characteristic

C₂×C₁₃

#504

yes

—

D₁₃

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#261

yes

characteristic

C₁₆

—

C₁₆

—

C₁₃

#2164

yes

characteristic, complemented, Sylow

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₁₃⋊C₈

yes

—

C₂×C₄

C₂²×#261

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×D₁₃⋊C₈

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

D₁₃⋊M₁₆

yes

characteristic

C₄

#88237

yes

characteristic

C₂

—

C₂

#11719049

yes

characteristic

100

C₂

#11719096

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₈
Fitting	C₁₃×#97	C₄
prime radical	C₂²×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂³
hypercenter	#97	#261
hypocenter	C₁₃	#2164
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#261

commutator, socle

C₂²×C₁₃

C₂²×C₈

Fitting

C₁₃×#97

C₄

prime radical

C₂²×D₁₃

C₂×C₈

C₂³

C₁₃

G ▷ C₂²×C₁₃ ▷ C₁₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
2. #11718260	C₂	semidirect
4. #11718231	C₂	semidirect
5. C₄×#6092	C₂	semidirect
78. C₁₃	#2164	semidirect

H ≅ G/N

type

2. #11718260

C₂

semidirect

4. #11718231

C₂

semidirect

5. C₄×#6092

C₂

semidirect

78. C₁₃

#2164

semidirect

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

subgroup	index
#11718369	2
#11718260	2
#11718259	2
#11718231	2
C₄×#6092	2
#2164	13

subgroup

index

Subgroups — #13131203

Conjugacy classes of subgroups

Complements

Maximal subgroups