Group #11765071 — subgroups

Subgroups — C₅×D₇×SD₁₆ #11765071

Order 1120.

136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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	C₅×Q₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₄×D₇	C₂	1	1	yes	maximal, characteristic
3	C₅×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1143	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1142	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1132	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×D₇	—	2	1	no	—
9	C₅×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
10	C₅×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₅×C₂²⋊D₇	—	2	1	no	—
12	C₅×D₂₈	C₂²	1	1	yes	characteristic
13	C₄×C₅×D₇	—	2	1	no	—
14	C₄×C₅×D₇	C₂²	1	1	yes	characteristic
15	C₅×Dic₁₄	—	2	1	no	—
16	C₅×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
17	C₅×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
18	C₅×C₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
19	D₇×SD₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×SD₁₆	—	7	1	no	maximal, Hall
21	C₂²×C₅×C₇	—	2	1	no	—
22	C₂×C₅×D₇	—	2	1	no	—
23	C₂×C₅×D₇	—	4	2	no	—
24	C₂×C₅×D₇	D₄	1	1	yes	characteristic
25	C₄×C₅×C₇	—	2	1	no	—
26	C₄×C₅×C₇	C₂³	1	1	yes	characteristic
27	C₅×Dic₇	—	2	1	no	—
28	C₅×Dic₇	D₄	1	1	yes	characteristic
29	Q₈×D₇	C₂×C₅	1	1	yes	characteristic, complemented
30	D₄×D₇	C₂×C₅	1	1	yes	characteristic
31	C₇×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
32	#1143	C₂×C₅	1	1	yes	characteristic, complemented
33	#1142	C₂×C₅	1	1	yes	characteristic, complemented
34	#1132	C₂×C₅	1	1	yes	characteristic, complemented
35	C₈×D₇	C₂×C₅	1	1	yes	characteristic, complemented
36	C₂×C₅×Q₈	—	7	1	no	—
37	C₂×C₅×D₄	—	7	1	no	—
38	C₅×SD₁₆	—	7	1	no	—
39	C₅×SD₁₆	—	7	1	no	—
40	C₅×SD₁₆	—	7	1	no	—
41	C₅×SD₁₆	D₇	1	1	yes	characteristic, direct product factor
42	C₂×C₅×C₈	—	7	1	no	—
43	C₂×C₅×C₇	—	4	1	no	—
44	C₂×C₅×C₇	C₂×D₄	1	1	yes	characteristic
45	C₅×D₇	—	4	1	no	—
46	C₅×D₇	SD₁₆	1	2	yes	direct product factor
47	C₂²×D₇	—	2	1	no	—
48	C₇×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
49	C₇×D₄	C₂²×C₅	1	1	yes	characteristic
50	C₂²⋊D₇	—	2	1	no	—
51	D₂₈	C₂²×C₅	1	1	yes	characteristic
52	C₄×D₇	—	2	1	no	—
53	C₄×D₇	C₂²×C₅	1	1	yes	characteristic
54	Dic₁₄	—	2	1	no	—
55	Dic₁₄	C₂²×C₅	1	1	yes	characteristic, complemented
56	C₇×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
57	C₇⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
58	C₂³×C₅	—	14	1	no	—
59	C₅×Q₈	—	7	1	no	—
60	C₅×Q₈	—	14	1	no	—
61	C₅×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
62	C₅×D₄	—	7	1	no	—
63	C₅×D₄	—	14	1	no	—
64	C₅×D₄	C₂×D₇	1	1	yes	characteristic
65	C₂×C₄×C₅	—	7	1	no	—
66	C₂×C₄×C₅	—	14	1	no	—
67	C₅×C₈	—	7	1	no	—
68	C₅×C₈	C₂×D₇	1	1	yes	characteristic, complemented
69	C₅×C₇	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
70	C₂×SD₁₆	—	7	1	no	Sylow
71	C₂²×C₇	—	2	1	no	—
72	C₂×D₇	—	2	1	no	—
73	C₂×D₇	—	4	2	no	—
74	C₂×D₇	C₅×D₄	1	1	yes	characteristic
75	C₄×C₇	—	2	1	no	—
76	C₄×C₇	C₂³×C₅	1	1	yes	characteristic
77	Dic₇	—	2	1	no	—
78	Dic₇	C₅×D₄	1	1	yes	characteristic
79	C₂²×C₅	—	2	1	no	—
80	C₂²×C₅	—	7	1	no	—
81	C₂²×C₅	—	14	1	no	—
82	C₂²×C₅	—	28	2	no	—
83	C₄×C₅	—	2	1	no	—
84	C₄×C₅	—	7	1	no	—
85	C₄×C₅	—	14	1	no	—
86	C₄×C₅	C₂²×D₇	1	1	yes	characteristic
87	C₂×Q₈	—	7	1	no	—
88	C₂×D₄	—	7	1	no	—
89	SD₁₆	—	7	1	no	—
90	SD₁₆	—	7	1	no	—
91	SD₁₆	—	7	1	no	—
92	SD₁₆	C₅×D₇	1	1	yes	characteristic, direct product factor
93	C₂×C₈	—	7	1	no	—
94	C₂×C₇	—	4	1	no	—
95	C₂×C₇	C₂×C₅×D₄	1	1	yes	characteristic
96	D₇	—	4	1	no	—
97	D₇	C₅×SD₁₆	1	2	yes	direct product factor
98	C₂×C₅	—	4	1	no	—
99	C₂×C₅	—	7	2	no	—
100	C₂×C₅	—	28	1	no	—
101	C₂×C₅	D₄×D₇	1	1	yes	characteristic
102	C₂³	—	14	1	no	—
103	Q₈	—	7	1	no	—
104	Q₈	—	14	1	no	—
105	Q₈	C₂×C₅×D₇	1	1	yes	characteristic, complemented
106	D₄	—	7	1	no	—
107	D₄	—	14	1	no	—
108	D₄	C₂×C₅×D₇	1	1	yes	characteristic
109	C₂×C₄	—	7	1	no	—
110	C₂×C₄	—	14	1	no	—
111	C₈	—	7	1	no	—
112	C₈	C₂×C₅×D₇	1	1	yes	characteristic, complemented
113	C₇	C₂×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
114	C₅	D₇×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
115	C₂²	—	2	1	no	—
116	C₂²	—	7	1	no	—
117	C₂²	—	14	1	no	—
118	C₂²	—	28	2	no	—
119	C₄	—	2	1	no	—
120	C₄	—	7	1	no	—
121	C₄	—	14	1	no	—
122	C₄	C₂²×C₅×D₇	1	1	yes	characteristic
123	C₂	—	4	1	no	—
124	C₂	—	7	2	no	—
125	C₂	—	28	1	no	—
126	C₂	C₅×D₄×D₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×Q₈×D₇

C₂

yes

maximal, characteristic, complemented

C₅×D₄×D₇

C₂

yes

maximal, characteristic

C₅×C₇×SD₁₆

C₂

yes

maximal, characteristic, complemented

C₅×#1143

C₂

yes

maximal, characteristic, complemented

C₅×#1142

C₂

yes

maximal, characteristic, complemented

C₅×#1132

C₂

yes

maximal, characteristic, complemented

C₅×C₈×D₇

C₂

yes

maximal, characteristic, complemented

C₂²×C₅×D₇

—

C₅×C₇×Q₈

C₂²

yes

characteristic, complemented

C₅×C₇×D₄

C₂²

yes

characteristic

C₅×C₂²⋊D₇

—

C₅×D₂₈

C₂²

yes

characteristic

C₄×C₅×D₇

—

C₄×C₅×D₇

C₂²

yes

characteristic

C₅×Dic₁₄

—

C₅×Dic₁₄

C₂²

yes

characteristic, complemented

C₅×C₇×C₈

C₂²

yes

characteristic, complemented

C₅×C₇⋊C₈

C₂²

yes

characteristic, complemented

D₇×SD₁₆

C₅

yes

maximal, characteristic, direct product factor, Hall

C₂×C₅×SD₁₆

—

maximal, Hall

C₂²×C₅×C₇

—

C₂×C₅×D₇

—

C₂×C₅×D₇

—

C₂×C₅×D₇

D₄

yes

characteristic

C₄×C₅×C₇

—

C₄×C₅×C₇

C₂³

yes

characteristic

C₅×Dic₇

—

C₅×Dic₇

D₄

yes

characteristic

Q₈×D₇

C₂×C₅

yes

characteristic, complemented

D₄×D₇

C₂×C₅

yes

characteristic

C₇×SD₁₆

C₂×C₅

yes

characteristic, complemented

#1143

C₂×C₅

yes

characteristic, complemented

#1142

C₂×C₅

yes

characteristic, complemented

#1132

C₂×C₅

yes

characteristic, complemented

C₈×D₇

C₂×C₅

yes

characteristic, complemented

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₅×SD₁₆

—

C₅×SD₁₆

—

C₅×SD₁₆

—

C₅×SD₁₆

D₇

yes

characteristic, direct product factor

C₂×C₅×C₈

—

C₂×C₅×C₇

—

C₂×C₅×C₇

C₂×D₄

yes

characteristic

C₅×D₇

—

C₅×D₇

SD₁₆

yes

direct product factor

C₂²×D₇

—

C₇×Q₈

C₂²×C₅

yes

characteristic, complemented

C₇×D₄

C₂²×C₅

yes

characteristic

C₂²⋊D₇

—

D₂₈

C₂²×C₅

yes

characteristic

C₄×D₇

—

C₄×D₇

C₂²×C₅

yes

characteristic

Dic₁₄

—

Dic₁₄

C₂²×C₅

yes

characteristic, complemented

C₇×C₈

C₂²×C₅

yes

characteristic, complemented

C₇⋊C₈

C₂²×C₅

yes

characteristic, complemented

C₂³×C₅

—

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

C₂×D₇

yes

characteristic, complemented

C₅×D₄

—

C₅×D₄

—

C₅×D₄

C₂×D₇

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₅×C₈

—

C₅×C₈

C₂×D₇

yes

characteristic, complemented

C₅×C₇

C₂×SD₁₆

yes

characteristic, complemented, Hall

C₂×SD₁₆

—

Sylow

C₂²×C₇

—

C₂×D₇

—

C₂×D₇

—

C₂×D₇

C₅×D₄

yes

characteristic

C₄×C₇

—

C₄×C₇

C₂³×C₅

yes

characteristic

Dic₇

—

Dic₇

C₅×D₄

yes

characteristic

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₂²×D₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

SD₁₆

C₅×D₇

yes

characteristic, direct product factor

C₂×C₈

—

C₂×C₇

—

C₂×C₇

C₂×C₅×D₄

yes

characteristic

D₇

—

D₇

C₅×SD₁₆

yes

direct product factor

C₂×C₅

—

C₂×C₅

—

100

C₂×C₅

—

101

C₂×C₅

D₄×D₇

yes

characteristic

102

C₂³

—

103

Q₈

—

104

Q₈

—

105

Q₈

C₂×C₅×D₇

yes

characteristic, complemented

106

D₄

—

107

D₄

—

108

D₄

C₂×C₅×D₇

yes

characteristic

109

C₂×C₄

—

110

C₂×C₄

—

111

C₈

—

112

C₈

C₂×C₅×D₇

yes

characteristic, complemented

113

C₇

C₂×C₅×SD₁₆

yes

characteristic, complemented, Sylow

114

C₅

D₇×SD₁₆

yes

characteristic, direct product factor, Sylow

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

C₂²×C₅×D₇

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₅×D₄×D₇

yes

characteristic

	subgroup	G/H
center	C₂×C₅	D₄×D₇
commutator, cosocle	C₄×C₇	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₇
Fitting	C₅×C₇×SD₁₆	C₂
socle	C₂×C₅×C₇	C₂×D₄
prime radical	C₅×D₄×D₇	C₂
hypercenter	C₅×SD₁₆	D₇
hypocenter	C₇	C₂×C₅×SD₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×SD₁₆

subgroup

G/H

center

C₂×C₅

D₄×D₇

commutator, cosocle

C₄×C₇

C₂³×C₅

Frattini

C₄

C₂²×C₅×D₇

Fitting

C₅×C₇×SD₁₆

C₂

socle

C₂×C₅×C₇

C₂×D₄

prime radical

C₅×D₄×D₇

C₂

hypercenter

C₅×SD₁₆

D₇

hypocenter

C₇

C₂×C₅×SD₁₆

LCS

G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇

UCS

C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×SD₁₆

N	H ≅ G/N	type
1. C₅×Q₈×D₇	C₂	semidirect
3. C₅×C₇×SD₁₆	C₂	semidirect
4. C₅×#1143	C₂	semidirect
5. C₅×#1142	C₂	semidirect
6. C₅×#1132	C₂	semidirect
7. C₅×C₈×D₇	C₂	semidirect
9. C₅×C₇×Q₈	C₂²	semidirect
16. C₅×Dic₁₄	C₂²	semidirect
17. C₅×C₇×C₈	C₂²	semidirect
18. C₅×C₇⋊C₈	C₂²	semidirect
19. D₇×SD₁₆	C₅	direct (N × H)
29. Q₈×D₇	C₂×C₅	semidirect
31. C₇×SD₁₆	C₂×C₅	semidirect
32. #1143	C₂×C₅	semidirect
33. #1142	C₂×C₅	semidirect
34. #1132	C₂×C₅	semidirect
35. C₈×D₇	C₂×C₅	semidirect
41. C₅×SD₁₆	D₇	direct (N × H)
46. C₅×D₇	SD₁₆	direct (N × H)
48. C₇×Q₈	C₂²×C₅	semidirect
55. Dic₁₄	C₂²×C₅	semidirect
56. C₇×C₈	C₂²×C₅	semidirect
57. C₇⋊C₈	C₂²×C₅	semidirect
61. C₅×Q₈	C₂×D₇	semidirect
68. C₅×C₈	C₂×D₇	semidirect
69. C₅×C₇	C₂×SD₁₆	semidirect
92. SD₁₆	C₅×D₇	direct (N × H)
97. D₇	C₅×SD₁₆	direct (N × H)
105. Q₈	C₂×C₅×D₇	semidirect
112. C₈	C₂×C₅×D₇	semidirect
113. C₇	C₂×C₅×SD₁₆	semidirect
114. C₅	D₇×SD₁₆	direct (N × H)

H ≅ G/N

type

1. C₅×Q₈×D₇

C₂

semidirect

3. C₅×C₇×SD₁₆

C₂

semidirect

4. C₅×#1143

C₂

semidirect

5. C₅×#1142

C₂

semidirect

6. C₅×#1132

C₂

semidirect

7. C₅×C₈×D₇

C₂

semidirect

9. C₅×C₇×Q₈

C₂²

semidirect

16. C₅×Dic₁₄

C₂²

semidirect

17. C₅×C₇×C₈

C₂²

semidirect

18. C₅×C₇⋊C₈

C₂²

semidirect

19. D₇×SD₁₆

C₅

direct (N × H)

29. Q₈×D₇

C₂×C₅

semidirect

31. C₇×SD₁₆

C₂×C₅

semidirect

32. #1143

C₂×C₅

semidirect

33. #1142

C₂×C₅

semidirect

34. #1132

C₂×C₅

semidirect

35. C₈×D₇

C₂×C₅

semidirect

41. C₅×SD₁₆

D₇

direct (N × H)

46. C₅×D₇

SD₁₆

direct (N × H)

48. C₇×Q₈

C₂²×C₅

semidirect

55. Dic₁₄

C₂²×C₅

semidirect

56. C₇×C₈

C₂²×C₅

semidirect

57. C₇⋊C₈

C₂²×C₅

semidirect

61. C₅×Q₈

C₂×D₇

semidirect

68. C₅×C₈

C₂×D₇

semidirect

69. C₅×C₇

C₂×SD₁₆

semidirect

92. SD₁₆

C₅×D₇

direct (N × H)

97. D₇

C₅×SD₁₆

direct (N × H)

105. Q₈

C₂×C₅×D₇

semidirect

112. C₈

C₂×C₅×D₇

semidirect

113. C₇

C₂×C₅×SD₁₆

semidirect

114. C₅

D₇×SD₁₆

direct (N × H)

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

subgroup	index
C₅×Q₈×D₇	2
C₅×D₄×D₇	2
C₅×C₇×SD₁₆	2
C₅×#1143	2
C₅×#1142	2
C₅×#1132	2
C₅×C₈×D₇	2
D₇×SD₁₆	5
C₂×C₅×SD₁₆	7

subgroup

index

C₅×Q₈×D₇

C₅×D₄×D₇

C₅×C₇×SD₁₆

C₅×#1143

C₅×#1142

C₅×#1132

C₅×C₈×D₇

D₇×SD₁₆

C₂×C₅×SD₁₆

Subgroups — C₅×D₇×SD₁₆ #11765071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D7×SD16 #11765071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₇×SD₁₆ #11765071