Group #20265137 — subgroups

Subgroups — C₂×#15692167 #20265137

Order 6464.

202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₂²×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692167	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₁	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₀₁	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₀₁	—	2	2	no	—
8	C₂×C₄×D₁₀₁	—	2	2	no	—
9	C₂×C₄×D₁₀₁	C₄	1	2	yes	—
10	C₂×C₄×D₁₀₁	C₂²	1	2	yes	—
11	C₂×#11717579	—	2	2	no	—
12	C₂×#11717579	C₂²	1	2	yes	complemented
13	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₁	—	2	2	no	—
15	C₂×C₈×C₁₀₁	C₂²	1	2	yes	complemented
16	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₁₀₁	—	2	2	no	—
18	C₂²×D₁₀₁	—	2	2	no	—
19	C₂²×D₁₀₁	C₈	1	4	yes	complemented
20	C₂²×D₁₀₁	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
23	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
24	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₁	—	2	2	no	—
26	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
27	C₄×D₁₀₁	—	2	4	no	—
28	C₄×D₁₀₁	—	2	2	no	—
29	C₄×D₁₀₁	—	2	2	no	—
30	C₈×C₁₀₁	—	2	2	no	—
31	#11717579	—	2	2	no	—
32	C₂²×C₁₀₁	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₁₀₁	C₂×C₈	1	2	yes	—
34	C₂²×C₁₀₁	M₁₆	1	2	yes	—
35	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₀₁	—	2	8	no	—
37	C₂×D₁₀₁	—	2	2	no	—
38	C₂×D₁₀₁	—	2	2	no	—
39	C₂×D₁₀₁	C₂×C₈	1	4	yes	complemented
40	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
41	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
42	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
43	Dic₁₀₁	—	2	2	no	—
44	C₂×C₁₀₁	C₂²⋊C₈	1	4	yes	complemented
45	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
47	C₂×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
48	D₁₀₁	—	2	4	no	—
49	C₁₀₁	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₂²⋊C₈	—	101	1	no	maximal, Sylow
51	C₂³×C₄	—	101	1	no	—
52	C₂²×C₈	—	101	1	no	—
53	C₂²×C₈	D₁₀₁	1	1	yes	characteristic, complemented
54	C₂²⋊C₈	—	101	4	no	—
55	C₂⁴	—	101	1	no	—
56	C₂²×C₄	—	101	1	no	—
57	C₂²×C₄	—	101	2	no	—
58	C₂²×C₄	—	101	2	no	—
59	C₂²×C₄	—	202	2	no	—
60	C₂²×C₄	—	202	2	no	—
61	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	101	2	no	—
64	C₂×C₈	—	202	2	no	—
65	C₂×C₈	C₂×D₁₀₁	1	2	yes	complemented
66	C₂³	—	101	4	no	—
67	C₂³	—	101	2	no	—
68	C₂³	—	202	2	no	—
69	C₂³	—	202	2	no	—
70	C₂³	C₄×D₁₀₁	1	1	yes	characteristic
71	C₂×C₄	—	101	2	no	—
72	C₂×C₄	—	202	2	no	—
73	C₂×C₄	—	202	4	no	—
74	C₂×C₄	—	202	2	no	—
75	C₂×C₄	—	202	2	no	—
76	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
77	C₂×C₄	D₄₀₄	1	2	yes	—
78	C₂×C₄	C₂²⋊D₁₀₁	1	2	yes	—
79	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	202	2	no	—
82	C₂²	—	101	4	no	—
83	C₂²	—	202	8	no	—
84	C₂²	—	202	2	no	—
85	C₂²	—	202	2	no	—
86	C₂²	#13108051	1	2	yes	—
87	C₂²	C₈×D₁₀₁	1	2	yes	—
88	C₂²	#13108057	1	2	yes	—
89	C₂²	C₂×C₄×D₁₀₁	1	1	yes	characteristic
90	C₄	—	202	2	no	—
91	C₄	#13108051	1	2	yes	—
92	C₄	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
93	C₄	C₂×D₄₀₄	1	1	yes	characteristic
94	C₂	—	202	4	no	—
95	C₂	#15692167	1	4	yes	direct product factor
96	C₂	C₂×#13108051	1	1	yes	characteristic
97	C₂	C₂×C₈×D₁₀₁	1	1	yes	characteristic
98	C₂	C₂×#13108057	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×D₁₀₁

C₂

yes

maximal, characteristic

C₂²×#11717579

C₂

yes

maximal, characteristic, complemented

#15692167

C₂

yes

maximal, direct product factor

C₂²×C₈×C₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₁

C₄

yes

characteristic

C₂²×Dic₁₀₁

C₄

yes

characteristic

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

C₄

yes

—

C₂×C₄×D₁₀₁

C₂²

yes

—

C₂×#11717579

—

C₂×#11717579

C₂²

yes

complemented

C₂²×C₄×C₁₀₁

C₂²

yes

characteristic

C₂×C₈×C₁₀₁

—

C₂×C₈×C₁₀₁

C₂²

yes

complemented

C₂³×C₁₀₁

C₂×C₄

yes

characteristic

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

C₈

yes

complemented

C₂²×D₁₀₁

C₂×C₄

yes

—

C₂×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₁

D₄

yes

—

C₂×C₄×C₁₀₁

D₄

yes

—

C₂×C₄×C₁₀₁

C₂³

yes

characteristic

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂×C₄

yes

—

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₈×C₁₀₁

—

#11717579

—

C₂²×C₁₀₁

C₂²⋊C₄

yes

—

C₂²×C₁₀₁

C₂×C₈

yes

—

C₂²×C₁₀₁

M₁₆

yes

—

C₂²×C₁₀₁

C₂²×C₄

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

—

C₂×D₁₀₁

C₂×C₈

yes

complemented

C₄×C₁₀₁

C₂²⋊C₄

yes

—

C₄×C₁₀₁

C₂×D₄

yes

characteristic

C₄×C₁₀₁

C₂×D₄

yes

characteristic

Dic₁₀₁

—

C₂×C₁₀₁

C₂²⋊C₈

yes

complemented

C₂×C₁₀₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₀₁

C₂²×C₈

yes

characteristic

C₂×C₁₀₁

C₂×M₁₆

yes

characteristic

D₁₀₁

—

C₁₀₁

C₂×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊C₈

—

101

maximal, Sylow

C₂³×C₄

—

101

—

C₂²×C₈

—

101

—

C₂²×C₈

D₁₀₁

yes

characteristic, complemented

C₂²⋊C₈

—

101

—

C₂⁴

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

C₂²×C₄

—

202

—

C₂²×C₄

—

202

—

C₂²×C₄

C₂×D₁₀₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

101

—

C₂×C₈

—

202

—

C₂×C₈

C₂×D₁₀₁

yes

complemented

C₂³

—

101

—

C₂³

—

101

—

C₂³

—

202

—

C₂³

—

202

—

C₂³

C₄×D₁₀₁

yes

characteristic

C₂×C₄

—

101

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

—

202

—

C₂×C₄

C₄×D₁₀₁

yes

characteristic

C₂×C₄

D₄₀₄

yes

—

C₂×C₄

C₂²⋊D₁₀₁

yes

—

C₂×C₄

C₂²×D₁₀₁

yes

characteristic

C₈

—

C₈

—

202

—

C₂²

—

101

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

—

202

—

C₂²

#13108051

yes

—

C₂²

C₈×D₁₀₁

yes

—

C₂²

#13108057

yes

—

C₂²

C₂×C₄×D₁₀₁

yes

characteristic

C₄

—

202

—

C₄

#13108051

yes

—

C₄

C₂×C₂²⋊D₁₀₁

yes

characteristic

C₄

C₂×D₄₀₄

yes

characteristic

C₂

—

202

—

C₂

#15692167

yes

direct product factor

C₂

C₂×#13108051

yes

characteristic

C₂

C₂×C₈×D₁₀₁

yes

characteristic

C₂

C₂×#13108057

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂²×C₈×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂×C₄
hypercenter	C₂²×C₈	D₁₀₁
hypocenter	C₁₀₁	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×D₁₀₁

commutator

C₂×C₁₀₁

C₂²×C₈

Frattini

C₂×C₄

C₂²×D₁₀₁

Fitting

C₂²×C₈×C₁₀₁

C₂

socle

C₂³×C₁₀₁

C₂×C₄

hypercenter

C₂²×C₈

D₁₀₁

hypocenter

C₁₀₁

C₂×C₂²⋊C₈

LCS

G ▷ C₂×C₁₀₁ ▷ C₁₀₁

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. C₂²×#11717579	C₂	semidirect
3. #15692167	C₂	direct (N × H)
4. C₂²×C₈×C₁₀₁	C₂	semidirect
12. C₂×#11717579	C₂²	semidirect
15. C₂×C₈×C₁₀₁	C₂²	semidirect
19. C₂²×D₁₀₁	C₈	semidirect
39. C₂×D₁₀₁	C₂×C₈	semidirect
44. C₂×C₁₀₁	C₂²⋊C₈	semidirect
49. C₁₀₁	C₂×C₂²⋊C₈	semidirect
53. C₂²×C₈	D₁₀₁	semidirect
65. C₂×C₈	C₂×D₁₀₁	semidirect
95. C₂	#15692167	direct (N × H)

H ≅ G/N

type

2. C₂²×#11717579

C₂

semidirect

3. #15692167

C₂

direct (N × H)

4. C₂²×C₈×C₁₀₁

C₂

semidirect

12. C₂×#11717579

C₂²

semidirect

15. C₂×C₈×C₁₀₁

C₂²

semidirect

19. C₂²×D₁₀₁

C₈

semidirect

39. C₂×D₁₀₁

C₂×C₈

semidirect

44. C₂×C₁₀₁

C₂²⋊C₈

semidirect

49. C₁₀₁

C₂×C₂²⋊C₈

semidirect

53. C₂²×C₈

D₁₀₁

semidirect

65. C₂×C₈

C₂×D₁₀₁

semidirect

95. C₂

#15692167

direct (N × H)

Subgroups — C₂×#15692167 #20265137

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15692167 #20265137

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692167 #20265137