Group #44477693 — subgroups

Subgroups — (C₅⋊(D₁₃⋊C₉))⋊D₁₃ #44477693

Order 30420.

136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 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⋊C₉×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₅⋊(D₁₃⋊C₉)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×(C₁₃⋊C₉)⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₆₅⋊D₁₃	C₃	1	1	yes	maximal, characteristic
5	C₅×C₁₃×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃×D₁₃⋊C₉	—	5	1	no	maximal, Hall
7	C₃×C₁₃×D₆₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₃×D₆₅	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic
10	D₆₅⋊D₁₃	C₉	1	1	yes	characteristic, complemented, Hall
11	D₁₃×C₁₃⋊C₉	—	5	1	no	—
12	(C₁₃⋊C₉)⋊D₁₃	D₅	1	1	yes	characteristic, complemented
13	C₁₃×D₁₃⋊C₉	—	5	1	no	—
14	C₃×C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic
15	C₉×D₅×D₁₃	—	13	1	no	maximal
16	D₅×D₁₃⋊C₉	—	13	1	no	maximal
17	C₃×D₁₃²	—	5	1	no	—
18	C₁₃×D₆₅	C₂×C₉	1	1	yes	characteristic, complemented
19	C₁₃×D₆₅	C₂×C₉	1	1	yes	characteristic, complemented
20	C₅×C₁₃⋊D₁₃	C₂×C₉	1	1	yes	characteristic, complemented
21	C₁₃×C₁₃⋊C₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
22	C₉×D₆₅	—	13	1	no	—
23	C₉×D₅×C₁₃	—	13	1	no	—
24	C₅×C₉×D₁₃	—	13	1	no	—
25	C₅⋊(D₁₃⋊C₉)	D₁₃	1	1	yes	characteristic, complemented
26	D₅×C₁₃⋊C₉	—	13	1	no	—
27	C₅×D₁₃⋊C₉	—	13	1	no	—
28	C₃×C₁₃⋊D₁₃	C₃×D₅	1	1	yes	characteristic
29	C₃×C₁₃×D₁₃	—	5	1	no	—
30	C₃×C₁₃×D₁₃	—	5	1	no	—
31	C₅×C₁₃²	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
32	C₃×D₅×D₁₃	—	13	1	no	—
33	C₃×D₅×D₁₃	—	39	1	no	—
34	D₁₃²	—	5	1	no	Hall
35	C₅×C₉×C₁₃	—	13	1	no	—
36	C₅×C₁₃⋊C₉	C₂×D₁₃	1	1	yes	characteristic, complemented
37	C₃×C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic
38	C₂×C₉×D₁₃	—	65	1	no	—
39	C₂×D₁₃⋊C₉	—	65	1	no	—
40	C₃×D₆₅	D₁₃⋊C₃	1	1	yes	characteristic
41	C₃×D₆₅	C₃×D₁₃	1	1	yes	characteristic
42	C₃×D₅×C₁₃	—	13	1	no	—
43	C₃×D₅×C₁₃	—	39	1	no	—
44	C₃×C₅×D₁₃	—	13	1	no	—
45	C₃×C₅×D₁₃	—	39	1	no	—
46	C₃×C₅×D₁₃	—	78	2	no	—
47	C₁₃⋊D₁₃	C₉×D₅	1	1	yes	characteristic, complemented
48	C₁₃×D₁₃	—	5	1	no	—
49	C₁₃×D₁₃	—	5	1	no	—
50	D₅×D₁₃	—	13	1	no	—
51	D₅×D₁₃	—	39	1	no	—
52	C₂×C₉×C₁₃	—	65	1	no	—
53	C₉×D₁₃	—	13	1	no	—
54	C₉×D₁₃	—	65	1	no	—
55	C₂×C₁₃⋊C₉	—	65	1	no	—
56	D₁₃⋊C₉	—	5	1	no	—
57	D₁₃⋊C₉	—	13	1	no	—
58	C₃×C₅×C₁₃	—	6	2	no	—
59	C₃×C₅×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic
60	C₃×C₅×C₁₃	C₂×C₃×D₁₃	1	1	yes	characteristic
61	C₂×C₉×D₅	—	169	1	no	Hall
62	C₁₃²	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₃×D₁₃	—	65	1	no	—
64	C₂×C₃×D₁₃	—	195	1	no	—
65	D₆₅	D₁₃⋊C₉	1	1	yes	characteristic, complemented
66	D₆₅	C₉×D₁₃	1	1	yes	characteristic, complemented
67	C₅×D₁₃	—	13	1	no	—
68	C₅×D₁₃	—	39	1	no	—
69	C₅×D₁₃	—	78	2	no	—
70	D₅×C₁₃	—	13	1	no	—
71	D₅×C₁₃	—	39	1	no	—
72	C₉×C₁₃	—	13	1	no	—
73	C₁₃⋊C₉	D₅×D₁₃	1	1	yes	characteristic, complemented
74	C₂×C₅×C₉	—	169	1	no	—
75	C₉×D₅	—	13	1	no	—
76	C₉×D₅	—	169	1	no	—
77	C₂×C₃×C₁₃	—	65	1	no	—
78	C₂×C₃×C₁₃	—	195	1	no	—
79	C₃×D₁₃	—	5	1	no	—
80	C₃×D₁₃	—	5	1	no	—
81	C₃×D₁₃	—	13	1	no	—
82	C₃×D₁₃	—	39	1	no	—
83	C₃×D₁₃	—	78	2	no	—
84	C₅×C₁₃	—	6	2	no	—
85	C₅×C₁₃	C₂×D₁₃⋊C₉	1	1	yes	characteristic, complemented
86	C₅×C₁₃	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented
87	C₂×C₃×D₅	—	507	1	no	—
88	C₂×D₁₃	—	65	1	no	—
89	C₂×D₁₃	—	195	1	no	—
90	C₅×C₉	—	13	1	no	Hall
91	C₃×C₁₃	—	6	2	no	—
92	C₃×C₁₃	D₅×D₁₃⋊C₃	1	1	yes	characteristic
93	C₃×C₁₃	C₃×D₅×D₁₃	1	1	yes	characteristic
94	C₂²×C₉	—	845	1	no	Hall
95	C₂×C₃×C₅	—	169	1	no	—
96	C₃×D₅	—	13	1	no	—
97	C₃×D₅	—	39	1	no	—
98	C₂×C₁₃	—	65	1	no	—
99	C₂×C₁₃	—	195	1	no	—
100	D₁₃	—	5	1	no	—
101	D₁₃	—	5	1	no	—
102	D₁₃	—	13	1	no	—
103	D₁₃	—	39	1	no	—
104	D₁₃	—	78	2	no	—
105	C₂×D₅	—	507	1	no	Hall
106	C₂×C₉	—	65	1	no	—
107	C₂×C₉	—	845	1	no	—
108	C₂×C₉	—	169	1	no	—
109	C₃×C₅	D₁₃×D₁₃⋊C₃	1	1	yes	characteristic
110	C₁₃	—	6	2	no	—
111	C₁₃	D₅×D₁₃⋊C₉	1	1	yes	characteristic, complemented
112	C₁₃	C₉×D₅×D₁₃	1	1	yes	characteristic, complemented
113	C₂²×C₃	—	2535	1	no	—
114	C₂×C₅	—	169	1	no	—
115	D₅	—	13	1	no	—
116	D₅	—	39	1	no	—
117	C₉	—	13	1	no	Sylow
118	C₂×C₃	—	65	1	no	—
119	C₂×C₃	—	195	1	no	—
120	C₂×C₃	—	507	1	no	—
121	C₅	D₁₃×D₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
122	C₂²	—	2535	1	no	Sylow
123	C₃	(C₅⋊(D₁₃⋊C₃))⋊D₁₃	1	1	yes	characteristic
124	C₂	—	65	1	no	—
125	C₂	—	195	1	no	—
126	C₂	—	507	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₃⋊C₉×D₆₅

C₂

yes

maximal, characteristic, complemented

C₁₃×C₅⋊(D₁₃⋊C₉)

C₂

yes

maximal, characteristic, complemented

C₅×(C₁₃⋊C₉)⋊D₁₃

C₂

yes

maximal, characteristic, complemented

C₃×D₆₅⋊D₁₃

C₃

yes

maximal, characteristic

C₅×C₁₃×C₁₃⋊C₉

C₂²

yes

characteristic, complemented, Hall

D₁₃×D₁₃⋊C₉

—

maximal, Hall

C₃×C₁₃×D₆₅

C₂×C₃

yes

characteristic

C₃×C₁₃×D₆₅

C₂×C₃

yes

characteristic

C₃×C₅×C₁₃⋊D₁₃

C₂×C₃

yes

characteristic

D₆₅⋊D₁₃

C₉

yes

characteristic, complemented, Hall

D₁₃×C₁₃⋊C₉

—

(C₁₃⋊C₉)⋊D₁₃

D₅

yes

characteristic, complemented

C₁₃×D₁₃⋊C₉

—

C₃×C₅×C₁₃²

C₂²×C₃

yes

characteristic

C₉×D₅×D₁₃

—

maximal

D₅×D₁₃⋊C₉

—

maximal

C₃×D₁₃²

—

C₁₃×D₆₅

C₂×C₉

yes

characteristic, complemented

C₁₃×D₆₅

C₂×C₉

yes

characteristic, complemented

C₅×C₁₃⋊D₁₃

C₂×C₉

yes

characteristic, complemented

C₁₃×C₁₃⋊C₉

C₂×D₅

yes

characteristic, complemented, Hall

C₉×D₆₅

—

C₉×D₅×C₁₃

—

C₅×C₉×D₁₃

—

C₅⋊(D₁₃⋊C₉)

D₁₃

yes

characteristic, complemented

D₅×C₁₃⋊C₉

—

C₅×D₁₃⋊C₉

—

C₃×C₁₃⋊D₁₃

C₃×D₅

yes

characteristic

C₃×C₁₃×D₁₃

—

C₃×C₁₃×D₁₃

—

C₅×C₁₃²

C₂²×C₉

yes

characteristic, complemented, Hall

C₃×D₅×D₁₃

—

C₃×D₅×D₁₃

—

D₁₃²

—

Hall

C₅×C₉×C₁₃

—

C₅×C₁₃⋊C₉

C₂×D₁₃

yes

characteristic, complemented

C₃×C₁₃²

C₂×C₃×D₅

yes

characteristic

C₂×C₉×D₁₃

—

C₂×D₁₃⋊C₉

—

C₃×D₆₅

D₁₃⋊C₃

yes

characteristic

C₃×D₆₅

C₃×D₁₃

yes

characteristic

C₃×D₅×C₁₃

—

C₃×D₅×C₁₃

—

C₃×C₅×D₁₃

—

C₃×C₅×D₁₃

—

C₃×C₅×D₁₃

—

C₁₃⋊D₁₃

C₉×D₅

yes

characteristic, complemented

C₁₃×D₁₃

—

C₁₃×D₁₃

—

D₅×D₁₃

—

D₅×D₁₃

—

C₂×C₉×C₁₃

—

C₉×D₁₃

—

C₉×D₁₃

—

C₂×C₁₃⋊C₉

—

D₁₃⋊C₉

—

D₁₃⋊C₉

—

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

C₂×D₁₃⋊C₃

yes

characteristic

C₃×C₅×C₁₃

C₂×C₃×D₁₃

yes

characteristic

C₂×C₉×D₅

—

169

Hall

C₁₃²

C₂×C₉×D₅

yes

characteristic, complemented, Sylow

C₂×C₃×D₁₃

—

C₂×C₃×D₁₃

—

195

—

D₆₅

D₁₃⋊C₉

yes

characteristic, complemented

D₆₅

C₉×D₁₃

yes

characteristic, complemented

C₅×D₁₃

—

C₅×D₁₃

—

C₅×D₁₃

—

D₅×C₁₃

—

D₅×C₁₃

—

C₉×C₁₃

—

C₁₃⋊C₉

D₅×D₁₃

yes

characteristic, complemented

C₂×C₅×C₉

—

169

—

C₉×D₅

—

C₉×D₅

—

169

—

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

—

195

—

C₃×D₁₃

—

C₃×D₁₃

—

C₃×D₁₃

—

C₃×D₁₃

—

C₃×D₁₃

—

C₅×C₁₃

—

C₅×C₁₃

C₂×D₁₃⋊C₉

yes

characteristic, complemented

C₅×C₁₃

C₂×C₉×D₁₃

yes

characteristic, complemented

C₂×C₃×D₅

—

507

—

C₂×D₁₃

—

C₂×D₁₃

—

195

—

C₅×C₉

—

Hall

C₃×C₁₃

—

C₃×C₁₃

D₅×D₁₃⋊C₃

yes

characteristic

C₃×C₁₃

C₃×D₅×D₁₃

yes

characteristic

C₂²×C₉

—

845

Hall

C₂×C₃×C₅

—

169

—

C₃×D₅

—

C₃×D₅

—

C₂×C₁₃

—

C₂×C₁₃

—

195

—

100

D₁₃

—

101

D₁₃

—

102

D₁₃

—

103

D₁₃

—

104

D₁₃

—

105

C₂×D₅

—

507

Hall

106

C₂×C₉

—

107

C₂×C₉

—

845

—

108

C₂×C₉

—

169

—

109

C₃×C₅

D₁₃×D₁₃⋊C₃

yes

characteristic

110

C₁₃

—

111

C₁₃

D₅×D₁₃⋊C₉

yes

characteristic, complemented

112

C₁₃

C₉×D₅×D₁₃

yes

characteristic, complemented

113

C₂²×C₃

—

2535

—

114

C₂×C₅

—

169

—

115

D₅

—

116

D₅

—

117

C₉

—

Sylow

118

C₂×C₃

—

119

C₂×C₃

—

195

—

120

C₂×C₃

—

507

—

121

C₅

D₁₃×D₁₃⋊C₉

yes

characteristic, complemented, Sylow

122

C₂²

—

2535

Sylow

123

C₃

(C₅⋊(D₁₃⋊C₃))⋊D₁₃

yes

characteristic

124

C₂

—

125

C₂

—

195

—

126

C₂

—

507

—

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₅⋊(D₁₃⋊C₃))⋊D₁₃
commutator, hypocenter	C₅×C₁₃²	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃²	C₂²×C₃
prime radical	C₃×D₆₅⋊D₁₃	C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₃

subgroup

G/H

center, Frattini, hypercenter

C₃

(C₅⋊(D₁₃⋊C₃))⋊D₁₃

commutator, hypocenter

C₅×C₁₃²

C₂²×C₉

Fitting, socle, cosocle

C₃×C₅×C₁₃²

C₂²×C₃

prime radical

C₃×D₆₅⋊D₁₃

C₃

LCS

G ▷ C₅×C₁₃²

UCS

C₁ ◁ C₃

N	H ≅ G/N	type
1. C₁₃⋊C₉×D₆₅	C₂	semidirect
2. C₁₃×C₅⋊(D₁₃⋊C₉)	C₂	semidirect
3. C₅×(C₁₃⋊C₉)⋊D₁₃	C₂	semidirect
5. C₅×C₁₃×C₁₃⋊C₉	C₂²	semidirect
10. D₆₅⋊D₁₃	C₉	semidirect
12. (C₁₃⋊C₉)⋊D₁₃	D₅	semidirect
18. C₁₃×D₆₅	C₂×C₉	semidirect
19. C₁₃×D₆₅	C₂×C₉	semidirect
20. C₅×C₁₃⋊D₁₃	C₂×C₉	semidirect
21. C₁₃×C₁₃⋊C₉	C₂×D₅	semidirect
25. C₅⋊(D₁₃⋊C₉)	D₁₃	semidirect
31. C₅×C₁₃²	C₂²×C₉	semidirect
36. C₅×C₁₃⋊C₉	C₂×D₁₃	semidirect
47. C₁₃⋊D₁₃	C₉×D₅	semidirect
62. C₁₃²	C₂×C₉×D₅	semidirect
65. D₆₅	D₁₃⋊C₉	semidirect
66. D₆₅	C₉×D₁₃	semidirect
73. C₁₃⋊C₉	D₅×D₁₃	semidirect
85. C₅×C₁₃	C₂×D₁₃⋊C₉	semidirect
86. C₅×C₁₃	C₂×C₉×D₁₃	semidirect
111. C₁₃	D₅×D₁₃⋊C₉	semidirect
112. C₁₃	C₉×D₅×D₁₃	semidirect
121. C₅	D₁₃×D₁₃⋊C₉	semidirect

H ≅ G/N

type

1. C₁₃⋊C₉×D₆₅

C₂

semidirect

2. C₁₃×C₅⋊(D₁₃⋊C₉)

C₂

semidirect

3. C₅×(C₁₃⋊C₉)⋊D₁₃

C₂

semidirect

5. C₅×C₁₃×C₁₃⋊C₉

C₂²

semidirect

10. D₆₅⋊D₁₃

C₉

semidirect

12. (C₁₃⋊C₉)⋊D₁₃

D₅

semidirect

18. C₁₃×D₆₅

C₂×C₉

semidirect

19. C₁₃×D₆₅

C₂×C₉

semidirect

20. C₅×C₁₃⋊D₁₃

C₂×C₉

semidirect

21. C₁₃×C₁₃⋊C₉

C₂×D₅

semidirect

25. C₅⋊(D₁₃⋊C₉)

D₁₃

semidirect

31. C₅×C₁₃²

C₂²×C₉

semidirect

36. C₅×C₁₃⋊C₉

C₂×D₁₃

semidirect

47. C₁₃⋊D₁₃

C₉×D₅

semidirect

62. C₁₃²

C₂×C₉×D₅

semidirect

65. D₆₅

D₁₃⋊C₉

semidirect

66. D₆₅

C₉×D₁₃

semidirect

73. C₁₃⋊C₉

D₅×D₁₃

semidirect

85. C₅×C₁₃

C₂×D₁₃⋊C₉

semidirect

86. C₅×C₁₃

C₂×C₉×D₁₃

semidirect

111. C₁₃

D₅×D₁₃⋊C₉

semidirect

112. C₁₃

C₉×D₅×D₁₃

semidirect

121. C₅

D₁₃×D₁₃⋊C₉

semidirect

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

subgroup	index
C₁₃⋊C₉×D₆₅	2
C₁₃×C₅⋊(D₁₃⋊C₉)	2
C₅×(C₁₃⋊C₉)⋊D₁₃	2
C₃×D₆₅⋊D₁₃	3
D₁₃×D₁₃⋊C₉	5
C₉×D₅×D₁₃	13
D₅×D₁₃⋊C₉	13

subgroup

index

C₁₃⋊C₉×D₆₅

C₁₃×C₅⋊(D₁₃⋊C₉)

C₅×(C₁₃⋊C₉)⋊D₁₃

C₃×D₆₅⋊D₁₃

D₁₃×D₁₃⋊C₉

C₉×D₅×D₁₃

D₅×D₁₃⋊C₉

Subgroups — (C₅⋊(D₁₃⋊C₉))⋊D₁₃ #44477693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C5⋊(D13⋊C9))⋊D13 #44477693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₅⋊(D₁₃⋊C₉))⋊D₁₃ #44477693