Group #30655151 — subgroups

Subgroups — D₅×C₁₃×D₆₃ #30655151

Order 16380.

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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	C₁₃×D₃₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₃×D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₅×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₁₃×D₂₁	—	3	1	no	maximal
5	C₅×C₇×C₉×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₃×D₆₃	—	5	1	no	maximal, Hall
7	C₁₃×D₁₀₅	—	3	1	no	—
8	C₅×C₁₃×D₂₁	—	3	1	no	—
9	C₃×C₇×D₅×C₁₃	D₃	1	1	yes	characteristic
10	D₅×C₁₃×D₉	—	7	1	no	maximal, Hall
11	D₅×C₁₃×D₇	—	9	1	no	Hall
12	C₂×C₇×C₉×C₁₃	—	5	1	no	—
13	C₁₃×D₆₃	—	5	1	no	—
14	C₁₃×D₆₃	D₅	1	1	yes	characteristic, direct product factor
15	C₃×C₅×C₇×C₁₃	C₂×D₃	1	1	yes	characteristic
16	D₅×D₆₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₁₃×D₄₅	—	7	1	no	—
18	C₅×C₁₃×D₉	—	7	1	no	—
19	C₉×D₅×C₁₃	D₇	1	1	yes	characteristic, complemented
20	C₂×C₁₃×D₂₁	—	15	1	no	—
21	C₁₃×D₃₅	—	9	1	no	—
22	C₇×D₅×C₁₃	D₉	1	1	yes	characteristic, complemented
23	C₅×C₁₃×D₇	—	9	1	no	—
24	C₇×C₉×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
25	D₃×D₅×C₁₃	—	21	1	no	—
26	D₃₁₅	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₅×D₆₃	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₇×C₉×D₅	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₅×C₉×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₇×C₁₃	—	5	1	no	—
31	C₁₃×D₂₁	—	3	1	no	—
32	C₁₃×D₂₁	—	15	1	no	—
33	C₂×C₁₃×D₉	—	35	1	no	Hall
34	C₅×C₇×C₁₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
35	D₅×D₂₁	—	3	1	no	—
36	C₁₃×D₁₅	—	21	1	no	—
37	C₅×D₃×C₁₃	—	21	1	no	—
38	C₃×D₅×C₁₃	D₂₁	1	1	yes	characteristic
39	C₂×C₁₃×D₇	—	45	1	no	Hall
40	C₅×C₇×C₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
41	C₃×C₇×C₁₃	D₃×D₅	1	1	yes	characteristic
42	C₂×D₅×C₁₃	—	63	1	no	Hall
43	C₂×D₆₃	—	5	1	no	Hall
44	C₂×C₉×C₁₃	—	5	1	no	—
45	C₁₃×D₉	—	7	1	no	—
46	C₁₃×D₉	—	35	1	no	—
47	D₁₀₅	—	3	1	no	—
48	C₅×D₂₁	—	3	1	no	—
49	C₃×C₇×D₅	D₃×C₁₃	1	1	yes	characteristic
50	C₃×C₅×C₁₃	C₂×D₂₁	1	1	yes	characteristic
51	C₂×C₇×C₁₃	—	5	1	no	—
52	C₁₃×D₇	—	9	1	no	—
53	C₁₃×D₇	—	45	1	no	—
54	D₅×D₉	—	7	1	no	Hall
55	C₂×D₃×C₁₃	—	105	1	no	—
56	D₅×D₇	—	9	1	no	Hall
57	C₂×C₅×C₁₃	—	63	1	no	—
58	D₅×C₁₃	—	63	1	no	—
59	D₅×C₁₃	D₆₃	1	1	yes	characteristic, direct product factor
60	C₂×C₇×C₉	—	5	1	no	—
61	D₆₃	—	5	1	no	—
62	D₆₃	D₅×C₁₃	1	1	yes	characteristic, direct product factor
63	C₉×C₁₃	D₅×D₇	1	1	yes	characteristic, complemented, Hall
64	C₃×C₅×C₇	C₂×D₃×C₁₃	1	1	yes	characteristic
65	C₇×C₁₃	D₅×D₉	1	1	yes	characteristic, complemented, Hall
66	D₄₅	—	7	1	no	—
67	C₉×D₅	C₁₃×D₇	1	1	yes	characteristic, complemented
68	C₅×D₉	—	7	1	no	—
69	C₂×D₂₁	—	15	1	no	—
70	C₂×C₃×C₁₃	—	5	1	no	—
71	D₃×C₁₃	—	21	1	no	—
72	D₃×C₁₃	—	105	1	no	—
73	D₃₅	—	9	1	no	—
74	C₅×D₇	—	9	1	no	—
75	C₇×D₅	C₁₃×D₉	1	1	yes	characteristic, complemented
76	C₅×C₁₃	C₂×D₆₃	1	1	yes	characteristic, complemented, Hall
77	C₇×C₉	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
78	D₃×D₅	—	21	1	no	—
79	C₂²×C₁₃	—	315	1	no	Hall
80	C₅×C₉	C₂×C₁₃×D₇	1	1	yes	characteristic, complemented, Hall
81	C₂×C₃×C₇	—	5	1	no	—
82	D₂₁	—	3	1	no	—
83	D₂₁	—	15	1	no	—
84	C₃×C₁₃	D₅×D₂₁	1	1	yes	characteristic
85	C₂×D₉	—	35	1	no	Hall
86	C₅×C₇	C₂×C₁₃×D₉	1	1	yes	characteristic, complemented, Hall
87	D₁₅	—	21	1	no	—
88	C₃×D₅	C₁₃×D₂₁	1	1	yes	characteristic
89	C₅×D₃	—	21	1	no	—
90	C₂×D₇	—	45	1	no	Hall
91	C₂×C₁₃	—	5	1	no	—
92	C₂×C₁₃	—	315	1	no	—
93	C₂×C₁₃	—	63	1	no	—
94	C₃×C₇	D₃×D₅×C₁₃	1	1	yes	characteristic
95	C₂×D₅	—	63	1	no	Hall
96	C₂×C₉	—	5	1	no	—
97	D₉	—	7	1	no	—
98	D₉	—	35	1	no	—
99	C₃×C₅	C₂×C₁₃×D₂₁	1	1	yes	characteristic
100	C₂×C₇	—	5	1	no	—
101	D₇	—	9	1	no	—
102	D₇	—	45	1	no	—
103	C₁₃	D₅×D₆₃	1	1	yes	characteristic, direct product factor, Sylow
104	C₂×D₃	—	105	1	no	—
105	C₂×C₅	—	63	1	no	—
106	D₅	—	63	1	no	—
107	D₅	C₁₃×D₆₃	1	1	yes	characteristic, direct product factor
108	C₉	D₅×C₁₃×D₇	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₅×C₁₃×D₉	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	5	1	no	—
111	D₃	—	21	1	no	—
112	D₃	—	105	1	no	—
113	C₅	C₂×C₁₃×D₆₃	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	315	1	no	Sylow
115	C₃	D₅×C₁₃×D₂₁	1	1	yes	characteristic
116	C₂	—	5	1	no	—
117	C₂	—	315	1	no	—
118	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃×D₃₁₅

C₂

yes

maximal, characteristic, complemented

C₅×C₁₃×D₆₃

C₂

yes

maximal, characteristic, complemented

C₇×C₉×D₅×C₁₃

C₂

yes

maximal, characteristic, complemented

D₅×C₁₃×D₂₁

—

maximal

C₅×C₇×C₉×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₁₃×D₆₃

—

maximal, Hall

C₁₃×D₁₀₅

—

C₅×C₁₃×D₂₁

—

C₃×C₇×D₅×C₁₃

D₃

yes

characteristic

D₅×C₁₃×D₉

—

maximal, Hall

D₅×C₁₃×D₇

—

Hall

C₂×C₇×C₉×C₁₃

—

C₁₃×D₆₃

—

C₁₃×D₆₃

D₅

yes

characteristic, direct product factor

C₃×C₅×C₇×C₁₃

C₂×D₃

yes

characteristic

D₅×D₆₃

C₁₃

yes

maximal, characteristic, direct product factor, Hall

C₁₃×D₄₅

—

C₅×C₁₃×D₉

—

C₉×D₅×C₁₃

D₇

yes

characteristic, complemented

C₂×C₁₃×D₂₁

—

C₁₃×D₃₅

—

C₇×D₅×C₁₃

D₉

yes

characteristic, complemented

C₅×C₁₃×D₇

—

C₇×C₉×C₁₃

C₂×D₅

yes

characteristic, complemented, Hall

D₃×D₅×C₁₃

—

D₃₁₅

C₂×C₁₃

yes

characteristic, complemented

C₅×D₆₃

C₂×C₁₃

yes

characteristic, complemented

C₇×C₉×D₅

C₂×C₁₃

yes

characteristic, complemented

C₅×C₉×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇×C₁₃

—

C₁₃×D₂₁

—

C₁₃×D₂₁

—

C₂×C₁₃×D₉

—

Hall

C₅×C₇×C₁₃

C₂×D₉

yes

characteristic, complemented, Hall

D₅×D₂₁

—

C₁₃×D₁₅

—

C₅×D₃×C₁₃

—

C₃×D₅×C₁₃

D₂₁

yes

characteristic

C₂×C₁₃×D₇

—

Hall

C₅×C₇×C₉

C₂²×C₁₃

yes

characteristic, complemented, Hall

C₃×C₇×C₁₃

D₃×D₅

yes

characteristic

C₂×D₅×C₁₃

—

Hall

C₂×D₆₃

—

Hall

C₂×C₉×C₁₃

—

C₁₃×D₉

—

C₁₃×D₉

—

D₁₀₅

—

C₅×D₂₁

—

C₃×C₇×D₅

D₃×C₁₃

yes

characteristic

C₃×C₅×C₁₃

C₂×D₂₁

yes

characteristic

C₂×C₇×C₁₃

—

C₁₃×D₇

—

C₁₃×D₇

—

D₅×D₉

—

Hall

C₂×D₃×C₁₃

—

105

—

D₅×D₇

—

Hall

C₂×C₅×C₁₃

—

D₅×C₁₃

—

D₅×C₁₃

D₆₃

yes

characteristic, direct product factor

C₂×C₇×C₉

—

D₆₃

—

D₆₃

D₅×C₁₃

yes

characteristic, direct product factor

C₉×C₁₃

D₅×D₇

yes

characteristic, complemented, Hall

C₃×C₅×C₇

C₂×D₃×C₁₃

yes

characteristic

C₇×C₁₃

D₅×D₉

yes

characteristic, complemented, Hall

D₄₅

—

C₉×D₅

C₁₃×D₇

yes

characteristic, complemented

C₅×D₉

—

C₂×D₂₁

—

C₂×C₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

—

105

—

D₃₅

—

C₅×D₇

—

C₇×D₅

C₁₃×D₉

yes

characteristic, complemented

C₅×C₁₃

C₂×D₆₃

yes

characteristic, complemented, Hall

C₇×C₉

C₂×D₅×C₁₃

yes

characteristic, complemented, Hall

D₃×D₅

—

C₂²×C₁₃

—

315

Hall

C₅×C₉

C₂×C₁₃×D₇

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

D₂₁

—

D₂₁

—

C₃×C₁₃

D₅×D₂₁

yes

characteristic

C₂×D₉

—

Hall

C₅×C₇

C₂×C₁₃×D₉

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

C₁₃×D₂₁

yes

characteristic

C₅×D₃

—

C₂×D₇

—

Hall

C₂×C₁₃

—

C₂×C₁₃

—

315

—

C₂×C₁₃

—

C₃×C₇

D₃×D₅×C₁₃

yes

characteristic

C₂×D₅

—

Hall

C₂×C₉

—

D₉

—

D₉

—

C₃×C₅

C₂×C₁₃×D₂₁

yes

characteristic

100

C₂×C₇

—

101

D₇

—

102

D₇

—

103

C₁₃

D₅×D₆₃

yes

characteristic, direct product factor, Sylow

104

C₂×D₃

—

105

—

105

C₂×C₅

—

106

D₅

—

107

D₅

C₁₃×D₆₃

yes

characteristic, direct product factor

108

C₉

D₅×C₁₃×D₇

yes

characteristic, complemented, Sylow

109

C₇

D₅×C₁₃×D₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

—

105

—

113

C₅

C₂×C₁₃×D₆₃

yes

characteristic, complemented, Sylow

114

C₂²

—

315

Sylow

115

C₃

D₅×C₁₃×D₂₁

yes

characteristic

116

C₂

—

117

C₂

—

315

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₁₃	D₅×D₆₃
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₁₃
Frattini	C₃	D₅×C₁₃×D₂₁
Fitting	C₅×C₇×C₉×C₁₃	C₂²
socle	C₃×C₅×C₇×C₁₃	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₁₃

subgroup

G/H

center, hypercenter

C₁₃

D₅×D₆₃

commutator, cosocle, hypocenter

C₅×C₇×C₉

C₂²×C₁₃

Frattini

C₃

D₅×C₁₃×D₂₁

Fitting

C₅×C₇×C₉×C₁₃

C₂²

socle

C₃×C₅×C₇×C₁₃

C₂×D₃

LCS

G ▷ C₅×C₇×C₉

UCS

C₁ ◁ C₁₃

N	H ≅ G/N	type
1. C₁₃×D₃₁₅	C₂	semidirect
2. C₅×C₁₃×D₆₃	C₂	semidirect
3. C₇×C₉×D₅×C₁₃	C₂	semidirect
5. C₅×C₇×C₉×C₁₃	C₂²	semidirect
14. C₁₃×D₆₃	D₅	direct (N × H)
16. D₅×D₆₃	C₁₃	direct (N × H)
19. C₉×D₅×C₁₃	D₇	semidirect
22. C₇×D₅×C₁₃	D₉	semidirect
24. C₇×C₉×C₁₃	C₂×D₅	semidirect
26. D₃₁₅	C₂×C₁₃	semidirect
27. C₅×D₆₃	C₂×C₁₃	semidirect
28. C₇×C₉×D₅	C₂×C₁₃	semidirect
29. C₅×C₉×C₁₃	C₂×D₇	semidirect
34. C₅×C₇×C₁₃	C₂×D₉	semidirect
40. C₅×C₇×C₉	C₂²×C₁₃	semidirect
59. D₅×C₁₃	D₆₃	direct (N × H)
62. D₆₃	D₅×C₁₃	direct (N × H)
63. C₉×C₁₃	D₅×D₇	semidirect
65. C₇×C₁₃	D₅×D₉	semidirect
67. C₉×D₅	C₁₃×D₇	semidirect
75. C₇×D₅	C₁₃×D₉	semidirect
76. C₅×C₁₃	C₂×D₆₃	semidirect
77. C₇×C₉	C₂×D₅×C₁₃	semidirect
80. C₅×C₉	C₂×C₁₃×D₇	semidirect
86. C₅×C₇	C₂×C₁₃×D₉	semidirect
103. C₁₃	D₅×D₆₃	direct (N × H)
107. D₅	C₁₃×D₆₃	direct (N × H)
108. C₉	D₅×C₁₃×D₇	semidirect
109. C₇	D₅×C₁₃×D₉	semidirect
113. C₅	C₂×C₁₃×D₆₃	semidirect

H ≅ G/N

type

1. C₁₃×D₃₁₅

C₂

semidirect

2. C₅×C₁₃×D₆₃

C₂

semidirect

3. C₇×C₉×D₅×C₁₃

C₂

semidirect

5. C₅×C₇×C₉×C₁₃

C₂²

semidirect

14. C₁₃×D₆₃

D₅

direct (N × H)

16. D₅×D₆₃

C₁₃

direct (N × H)

19. C₉×D₅×C₁₃

D₇

semidirect

22. C₇×D₅×C₁₃

D₉

semidirect

24. C₇×C₉×C₁₃

C₂×D₅

semidirect

26. D₃₁₅

C₂×C₁₃

semidirect

27. C₅×D₆₃

C₂×C₁₃

semidirect

28. C₇×C₉×D₅

C₂×C₁₃

semidirect

29. C₅×C₉×C₁₃

C₂×D₇

semidirect

34. C₅×C₇×C₁₃

C₂×D₉

semidirect

40. C₅×C₇×C₉

C₂²×C₁₃

semidirect

59. D₅×C₁₃

D₆₃

direct (N × H)

62. D₆₃

D₅×C₁₃

direct (N × H)

63. C₉×C₁₃

D₅×D₇

semidirect

65. C₇×C₁₃

D₅×D₉

semidirect

67. C₉×D₅

C₁₃×D₇

semidirect

75. C₇×D₅

C₁₃×D₉

semidirect

76. C₅×C₁₃

C₂×D₆₃

semidirect

77. C₇×C₉

C₂×D₅×C₁₃

semidirect

80. C₅×C₉

C₂×C₁₃×D₇

semidirect

86. C₅×C₇

C₂×C₁₃×D₉

semidirect

103. C₁₃

D₅×D₆₃

direct (N × H)

107. D₅

C₁₃×D₆₃

direct (N × H)

108. C₉

D₅×C₁₃×D₇

semidirect

109. C₇

D₅×C₁₃×D₉

semidirect

113. C₅

C₂×C₁₃×D₆₃

semidirect

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

subgroup	index
C₁₃×D₃₁₅	2
C₅×C₁₃×D₆₃	2
C₇×C₉×D₅×C₁₃	2
D₅×C₁₃×D₂₁	3
C₂×C₁₃×D₆₃	5
D₅×C₁₃×D₉	7
D₅×D₆₃	13

subgroup

index

C₁₃×D₃₁₅

C₅×C₁₃×D₆₃

C₇×C₉×D₅×C₁₃

D₅×C₁₃×D₂₁

C₂×C₁₃×D₆₃

D₅×C₁₃×D₉

D₅×D₆₃

Subgroups — D₅×C₁₃×D₆₃ #30655151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D5×C13×D63 #30655151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₁₃×D₆₃ #30655151