Group #30685610 — subgroups

Subgroups — D₄₅⋊D₉₅ #30685610

Order 17100.

144 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 34 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×D₈₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₅⋊D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊D₉₅	—	3	1	no	maximal
5	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₄₅⋊D₁₉	—	5	1	no	maximal
7	D₉×D₉₅	—	5	1	no	maximal
8	C₅×D₂₈₅	—	3	1	no	—
9	C₅×C₁₉×D₁₅	—	3	1	no	—
10	C₃×C₅⋊D₉₅	D₃	1	1	yes	characteristic
11	D₅×D₉₅	—	9	1	no	Hall
12	D₈₅₅	D₅	1	1	yes	characteristic, complemented
13	C₁₉×D₄₅	D₅	1	1	yes	characteristic, complemented
14	C₅×D₁₇₁	—	5	1	no	—
15	C₅×D₉×C₁₉	—	5	1	no	—
16	C₉×D₉₅	—	5	1	no	—
17	C₉×D₉₅	—	5	1	no	—
18	C₉×D₉₅	—	10	2	no	—
19	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
20	D₁₅⋊D₁₉	—	15	1	no	—
21	D₃×D₉₅	—	15	1	no	—
22	C₅⋊D₉₅	D₉	1	1	yes	characteristic, complemented
23	C₅×D₉₅	—	9	1	no	—
24	C₅×D₅×C₁₉	—	9	1	no	—
25	D₄₅⋊D₅	—	19	1	no	maximal, Hall
26	C₅×C₉×C₁₉	—	2	2	no	—
27	C₅×C₉×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
28	C₅×C₉×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
29	D₉×D₁₉	—	25	1	no	Hall
30	D₂₈₅	—	3	1	no	—
31	C₁₉×D₁₅	—	3	1	no	—
32	C₅×D₅₇	—	15	1	no	—
33	C₅×D₃×C₁₉	—	15	1	no	—
34	C₃×D₉₅	—	5	1	no	—
35	C₃×D₉₅	—	5	1	no	—
36	C₃×D₉₅	—	10	2	no	—
37	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
38	C₅×D₄₅	—	19	1	no	—
39	C₅×D₄₅	D₁₉	1	1	yes	characteristic, complemented
40	C₉×C₅⋊D₅	—	19	1	no	—
41	C₂×D₉₅	—	45	1	no	—
42	D₅×D₁₉	—	45	1	no	—
43	D₁₇₁	—	5	1	no	—
44	C₉×D₁₉	—	25	1	no	—
45	D₉×C₁₉	—	5	1	no	—
46	D₁₅⋊D₅	—	57	1	no	—
47	C₃×C₅×C₁₉	—	2	2	no	—
48	C₃×C₅×C₁₉	D₃×D₅	1	1	yes	characteristic
49	C₃×C₅×C₁₉	D₃×D₅	1	1	yes	characteristic
50	D₃×D₁₉	—	75	1	no	—
51	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
52	C₂×C₅×C₁₉	—	45	1	no	—
53	D₉₅	—	5	1	no	—
54	D₉₅	—	5	1	no	—
55	D₉₅	—	9	1	no	—
56	D₉₅	—	10	2	no	—
57	C₅×D₁₉	—	45	1	no	—
58	D₅×C₁₉	—	9	1	no	—
59	D₅×D₉	—	95	1	no	—
60	D₅×D₉	—	95	1	no	—
61	C₉×C₁₉	D₅²	1	1	yes	characteristic, complemented, Hall
62	C₅×D₁₅	—	3	1	no	—
63	C₅×D₁₅	—	57	1	no	—
64	C₃×C₅⋊D₅	—	19	1	no	—
65	D₅₇	—	15	1	no	—
66	C₃×D₁₉	—	25	1	no	—
67	D₃×C₁₉	—	15	1	no	—
68	D₅²	—	171	1	no	Hall
69	C₅×C₁₉	—	2	2	no	—
70	C₅×C₁₉	D₅×D₉	1	1	yes	characteristic, complemented
71	C₅×C₁₉	D₅×D₉	1	1	yes	characteristic, complemented
72	D₄₅	—	19	1	no	—
73	D₄₅	D₉₅	1	1	yes	characteristic, complemented
74	C₉×D₅	—	95	1	no	—
75	C₉×D₅	—	95	1	no	—
76	C₉×D₅	—	190	2	no	—
77	C₅×D₉	—	5	1	no	—
78	C₅×D₉	—	95	1	no	—
79	C₂×D₁₉	—	225	1	no	Hall
80	C₃×C₅²	D₃×D₁₉	1	1	yes	characteristic
81	D₃×D₅	—	285	1	no	—
82	D₃×D₅	—	285	1	no	—
83	C₃×C₁₉	D₁₅⋊D₅	1	1	yes	characteristic
84	C₅⋊D₅	—	19	1	no	—
85	C₅×D₅	—	9	1	no	—
86	C₅×D₅	—	171	1	no	—
87	C₅×C₉	—	2	2	no	—
88	C₅×C₉	D₅×D₁₉	1	1	yes	characteristic, complemented
89	C₅×C₉	C₂×D₉₅	1	1	yes	characteristic, complemented
90	C₂×C₁₉	—	45	1	no	—
91	D₁₉	—	25	1	no	—
92	D₁₉	—	45	1	no	—
93	C₂×D₉	—	475	1	no	Hall
94	D₁₅	—	3	1	no	—
95	D₁₅	—	57	1	no	—
96	C₃×D₅	—	95	1	no	—
97	C₃×D₅	—	95	1	no	—
98	C₃×D₅	—	190	2	no	—
99	C₅×D₃	—	15	1	no	—
100	C₅×D₃	—	285	1	no	—
101	C₅²	D₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
102	C₂×D₅	—	855	1	no	—
103	C₂×D₅	—	855	1	no	—
104	C₁₉	D₄₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
105	C₂×C₉	—	475	1	no	—
106	D₉	—	5	1	no	—
107	D₉	—	95	1	no	—
108	C₃×C₅	—	2	2	no	—
109	C₃×C₅	D₃×D₉₅	1	1	yes	characteristic
110	C₃×C₅	D₁₅⋊D₁₉	1	1	yes	characteristic
111	C₂×D₃	—	1425	1	no	—
112	C₂×C₅	—	45	1	no	—
113	C₂×C₅	—	855	1	no	—
114	D₅	—	9	1	no	—
115	D₅	—	95	1	no	—
116	D₅	—	95	1	no	—
117	D₅	—	171	1	no	—
118	D₅	—	190	2	no	—
119	C₉	D₅×D₉₅	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₃	—	475	1	no	—
121	D₃	—	15	1	no	—
122	D₃	—	285	1	no	—
123	C₅	—	2	2	no	—
124	C₅	D₉×D₉₅	1	1	yes	characteristic, complemented
125	C₅	D₄₅⋊D₁₉	1	1	yes	characteristic, complemented
126	C₂²	—	4275	1	no	Sylow
127	C₃	D₁₅⋊D₉₅	1	1	yes	characteristic
128	C₂	—	45	1	no	—
129	C₂	—	855	1	no	—
130	C₂	—	475	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×D₈₅₅

C₂

yes

maximal, characteristic, complemented

C₅×C₁₉×D₄₅

C₂

yes

maximal, characteristic, complemented

C₉×C₅⋊D₉₅

C₂

yes

maximal, characteristic, complemented

D₁₅⋊D₉₅

—

maximal

C₅²×C₉×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₄₅⋊D₁₉

—

maximal

D₉×D₉₅

—

maximal

C₅×D₂₈₅

—

C₅×C₁₉×D₁₅

—

C₃×C₅⋊D₉₅

D₃

yes

characteristic

D₅×D₉₅

—

Hall

D₈₅₅

D₅

yes

characteristic, complemented

C₁₉×D₄₅

D₅

yes

characteristic, complemented

C₅×D₁₇₁

—

C₅×D₉×C₁₉

—

C₉×D₉₅

—

C₉×D₉₅

—

C₉×D₉₅

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic

D₁₅⋊D₁₉

—

D₃×D₉₅

—

C₅⋊D₉₅

D₉

yes

characteristic, complemented

C₅×D₉₅

—

C₅×D₅×C₁₉

—

D₄₅⋊D₅

—

maximal, Hall

C₅×C₉×C₁₉

—

C₅×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented

C₅×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented

D₉×D₁₉

—

Hall

D₂₈₅

—

C₁₉×D₁₅

—

C₅×D₅₇

—

C₅×D₃×C₁₉

—

C₃×D₉₅

—

C₃×D₉₅

—

C₃×D₉₅

—

C₅²×C₁₉

C₂×D₉

yes

characteristic, complemented, Hall

C₅×D₄₅

—

C₅×D₄₅

D₁₉

yes

characteristic, complemented

C₉×C₅⋊D₅

—

C₂×D₉₅

—

D₅×D₁₉

—

D₁₇₁

—

C₉×D₁₉

—

D₉×C₁₉

—

D₁₅⋊D₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

D₃×D₅

yes

characteristic

C₃×C₅×C₁₉

D₃×D₅

yes

characteristic

D₃×D₁₉

—

C₅²×C₉

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

D₉₅

—

D₉₅

—

D₉₅

—

D₉₅

—

C₅×D₁₉

—

D₅×C₁₉

—

D₅×D₉

—

D₅×D₉

—

C₉×C₁₉

D₅²

yes

characteristic, complemented, Hall

C₅×D₁₅

—

C₅×D₁₅

—

C₃×C₅⋊D₅

—

D₅₇

—

C₃×D₁₉

—

D₃×C₁₉

—

D₅²

—

171

Hall

C₅×C₁₉

—

C₅×C₁₉

D₅×D₉

yes

characteristic, complemented

C₅×C₁₉

D₅×D₉

yes

characteristic, complemented

D₄₅

—

D₄₅

D₉₅

yes

characteristic, complemented

C₉×D₅

—

C₉×D₅

—

C₉×D₅

—

190

—

C₅×D₉

—

C₅×D₉

—

C₂×D₁₉

—

225

Hall

C₃×C₅²

D₃×D₁₉

yes

characteristic

D₃×D₅

—

285

—

D₃×D₅

—

285

—

C₃×C₁₉

D₁₅⋊D₅

yes

characteristic

C₅⋊D₅

—

C₅×D₅

—

C₅×D₅

—

171

—

C₅×C₉

—

C₅×C₉

D₅×D₁₉

yes

characteristic, complemented

C₅×C₉

C₂×D₉₅

yes

characteristic, complemented

C₂×C₁₉

—

D₁₉

—

D₁₉

—

C₂×D₉

—

475

Hall

D₁₅

—

D₁₅

—

C₃×D₅

—

C₃×D₅

—

C₃×D₅

—

190

—

C₅×D₃

—

100

C₅×D₃

—

285

—

101

C₅²

D₉×D₁₉

yes

characteristic, complemented, Sylow

102

C₂×D₅

—

855

—

103

C₂×D₅

—

855

—

104

C₁₉

D₄₅⋊D₅

yes

characteristic, complemented, Sylow

105

C₂×C₉

—

475

—

106

D₉

—

107

D₉

—

108

C₃×C₅

—

109

C₃×C₅

D₃×D₉₅

yes

characteristic

110

C₃×C₅

D₁₅⋊D₁₉

yes

characteristic

111

C₂×D₃

—

1425

—

112

C₂×C₅

—

113

C₂×C₅

—

855

—

114

D₅

—

115

D₅

—

116

D₅

—

117

D₅

—

171

—

118

D₅

—

190

—

119

C₉

D₅×D₉₅

yes

characteristic, complemented, Sylow

120

C₂×C₃

—

475

—

121

D₃

—

122

D₃

—

285

—

123

C₅

—

124

C₅

D₉×D₉₅

yes

characteristic, complemented

125

C₅

D₄₅⋊D₁₉

yes

characteristic, complemented

126

C₂²

—

4275

Sylow

127

C₃

D₁₅⋊D₉₅

yes

characteristic

128

C₂

—

129

C₂

—

855

—

130

C₂

—

475

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₉×C₁₉	C₂²
Frattini	C₃	D₁₅⋊D₉₅
socle	C₃×C₅²×C₁₉	C₂×D₃
LCS	G ▷ C₅²×C₉×C₁₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₅²×C₉×C₁₉

C₂²

Frattini

C₃

D₁₅⋊D₉₅

socle

C₃×C₅²×C₁₉

C₂×D₃

LCS

G ▷ C₅²×C₉×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. C₅×D₈₅₅	C₂	semidirect
2. C₅×C₁₉×D₄₅	C₂	semidirect
3. C₉×C₅⋊D₉₅	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
12. D₈₅₅	D₅	semidirect
13. C₁₉×D₄₅	D₅	semidirect
22. C₅⋊D₉₅	D₉	semidirect
27. C₅×C₉×C₁₉	C₂×D₅	semidirect
28. C₅×C₉×C₁₉	C₂×D₅	semidirect
37. C₅²×C₁₉	C₂×D₉	semidirect
39. C₅×D₄₅	D₁₉	semidirect
51. C₅²×C₉	C₂×D₁₉	semidirect
61. C₉×C₁₉	D₅²	semidirect
70. C₅×C₁₉	D₅×D₉	semidirect
71. C₅×C₁₉	D₅×D₉	semidirect
73. D₄₅	D₉₅	semidirect
88. C₅×C₉	D₅×D₁₉	semidirect
89. C₅×C₉	C₂×D₉₅	semidirect
101. C₅²	D₉×D₁₉	semidirect
104. C₁₉	D₄₅⋊D₅	semidirect
119. C₉	D₅×D₉₅	semidirect
124. C₅	D₉×D₉₅	semidirect
125. C₅	D₄₅⋊D₁₉	semidirect

H ≅ G/N

type

1. C₅×D₈₅₅

C₂

semidirect

2. C₅×C₁₉×D₄₅

C₂

semidirect

3. C₉×C₅⋊D₉₅

C₂

semidirect

5. C₅²×C₉×C₁₉

C₂²

semidirect

12. D₈₅₅

D₅

semidirect

13. C₁₉×D₄₅

D₅

semidirect

22. C₅⋊D₉₅

D₉

semidirect

27. C₅×C₉×C₁₉

C₂×D₅

semidirect

28. C₅×C₉×C₁₉

C₂×D₅

semidirect

37. C₅²×C₁₉

C₂×D₉

semidirect

39. C₅×D₄₅

D₁₉

semidirect

51. C₅²×C₉

C₂×D₁₉

semidirect

61. C₉×C₁₉

D₅²

semidirect

70. C₅×C₁₉

D₅×D₉

semidirect

71. C₅×C₁₉

D₅×D₉

semidirect

73. D₄₅

D₉₅

semidirect

88. C₅×C₉

D₅×D₁₉

semidirect

89. C₅×C₉

C₂×D₉₅

semidirect

101. C₅²

D₉×D₁₉

semidirect

104. C₁₉

D₄₅⋊D₅

semidirect

119. C₉

D₅×D₉₅

semidirect

124. C₅

D₉×D₉₅

semidirect

125. C₅

D₄₅⋊D₁₉

semidirect

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

subgroup	index
C₅×D₈₅₅	2
C₅×C₁₉×D₄₅	2
C₉×C₅⋊D₉₅	2
D₁₅⋊D₉₅	3
D₄₅⋊D₁₉	5
D₉×D₉₅	5
D₄₅⋊D₅	19

subgroup

index

C₅×D₈₅₅

C₅×C₁₉×D₄₅

C₉×C₅⋊D₉₅

D₁₅⋊D₉₅

D₄₅⋊D₁₉

D₉×D₉₅

D₄₅⋊D₅

Subgroups — D₄₅⋊D₉₅ #30685610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D45⋊D95 #30685610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₅⋊D₉₅ #30685610