Group #30685883 — subgroups

Subgroups — C₃×D₃×C₁₉×C₅⋊D₅ #30685883

Order 17100.

352 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 112 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	C₃×C₁₉×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅²×D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₁₉×C₅⋊D₅	—	3	1	no	maximal
5	D₃×C₁₉×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃×D₅×C₁₉	—	5	6	no	maximal
8	C₁₉×C₃⋊(C₅⋊D₅)	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅²×D₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₁₉×C₅⋊D₅	—	2	1	no	—
11	C₃×C₁₉×C₅⋊D₅	—	3	1	no	—
12	C₃×C₁₉×C₅⋊D₅	D₃	1	1	yes	characteristic, direct product factor
13	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅²×C₁₉	—	3	1	no	—
15	C₂×C₁₉×C₅⋊D₅	—	3	1	no	Hall
16	C₃×C₁₉×D₁₅	—	5	6	no	—
17	C₃×C₅×D₃×C₁₉	D₅	1	6	yes	complemented
18	C₃²×D₅×C₁₉	—	5	6	no	—
19	C₃×C₅²×C₁₉	—	2	1	no	—
20	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₅×C₁₉	—	15	6	no	—
23	D₃×D₅×C₁₉	—	5	6	no	—
24	C₂×C₅²×C₁₉	—	3	1	no	—
25	C₁₉×C₅⋊D₅	—	3	1	no	—
26	C₁₉×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic, direct product factor
27	C₃×D₃×C₅⋊D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₃²×C₅×C₁₉	C₂×D₅	1	6	yes	complemented
29	C₂×C₃×D₃×C₁₉	—	25	1	no	Hall
30	C₂×C₃×C₅×C₁₉	—	3	6	no	—
31	C₁₉×D₁₅	—	5	6	no	—
32	C₅×D₃×C₁₉	C₃×D₅	1	6	yes	complemented
33	C₃×D₅×C₁₉	—	5	6	no	—
34	C₃×D₅×C₁₉	—	5	6	no	—
35	C₃×D₅×C₁₉	—	10	6	no	—
36	C₃×D₅×C₁₉	—	15	6	no	—
37	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
38	C₃×C₃⋊(C₅⋊D₅)	C₂×C₁₉	1	1	yes	characteristic, complemented
39	C₃×C₅²×D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
40	C₃²×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic, complemented
41	C₂×D₅×C₁₉	—	15	6	no	—
42	C₂×C₃²×C₁₉	—	25	1	no	—
43	C₃×D₃×C₁₉	—	25	1	no	—
44	C₃×D₃×C₁₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
45	C₂×C₃×C₅⋊D₅	—	3	1	no	—
46	D₃×C₅⋊D₅	C₃×C₁₉	1	1	yes	characteristic, direct product factor
47	C₃×C₅×C₁₉	—	2	6	no	—
48	C₃×C₅×C₁₉	D₃×D₅	1	6	yes	complemented
49	C₃×C₅×C₁₉	C₂×C₃×D₅	1	6	yes	complemented
50	C₂²×C₃×C₁₉	—	75	1	no	—
51	C₂×D₃×C₁₉	—	25	1	no	—
52	C₃²×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
53	C₂×C₅×C₁₉	—	3	6	no	—
54	D₅×C₁₉	—	5	6	no	—
55	D₅×C₁₉	—	15	6	no	—
56	C₃×D₃×D₅	—	5	6	no	—
57	C₃²×C₁₉	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
58	C₂×C₃×C₅²	—	3	1	no	—
59	C₃⋊(C₅⋊D₅)	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
60	C₅²×D₃	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
61	C₃×C₅⋊D₅	—	2	1	no	—
62	C₃×C₅⋊D₅	—	3	1	no	—
63	C₃×C₅⋊D₅	D₃×C₁₉	1	1	yes	characteristic, direct product factor
64	C₃×C₅⋊D₅	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
65	C₂×C₃×C₁₉	—	3	1	no	—
66	C₂×C₃×C₁₉	—	25	1	no	—
67	C₂×C₃×C₁₉	—	25	1	no	—
68	C₂×C₃×C₁₉	—	50	1	no	—
69	C₂×C₃×C₁₉	—	75	1	no	—
70	D₃×C₁₉	—	25	1	no	—
71	D₃×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
72	C₂×C₅⋊D₅	—	3	1	no	Hall
73	C₅×C₁₉	C₃×D₃×D₅	1	6	yes	complemented
74	C₃×D₁₅	—	5	6	no	—
75	C₃×C₅×D₃	D₅×C₁₉	1	6	yes	complemented
76	C₃²×D₅	—	5	6	no	—
77	C₂²×C₁₉	—	75	1	no	Hall
78	C₃×C₅²	—	2	1	no	—
79	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic, complemented
80	C₃×C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
81	C₂×C₃×D₅	—	15	6	no	—
82	D₃×D₅	—	5	6	no	—
83	C₃×C₁₉	—	2	1	no	—
84	C₃×C₁₉	D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
85	C₃×C₁₉	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
86	C₂×C₅²	—	3	1	no	—
87	C₅⋊D₅	—	3	1	no	—
88	C₅⋊D₅	C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor
89	C₃²×C₅	C₂×D₅×C₁₉	1	6	yes	complemented
90	C₂×C₁₉	—	3	1	no	—
91	C₂×C₁₉	—	25	1	no	—
92	C₂×C₁₉	—	75	1	no	—
93	C₂×C₃×D₃	—	25	1	no	Hall
94	C₂×C₃×C₅	—	3	6	no	—
95	D₁₅	—	5	6	no	—
96	C₃×D₅	—	5	6	no	—
97	C₃×D₅	—	5	6	no	—
98	C₃×D₅	—	10	6	no	—
99	C₃×D₅	—	15	6	no	—
100	C₅×D₃	C₃×D₅×C₁₉	1	6	yes	complemented
101	C₅²	C₂×C₃×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
102	C₂×D₅	—	15	6	no	—
103	C₁₉	C₃×D₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
104	C₂×C₃²	—	25	1	no	—
105	C₃×D₃	—	25	1	no	—
106	C₃×D₃	C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
107	C₃×C₅	—	2	6	no	—
108	C₃×C₅	D₃×D₅×C₁₉	1	6	yes	complemented
109	C₃×C₅	C₂×C₃×D₅×C₁₉	1	6	yes	complemented
110	C₂²×C₃	—	75	1	no	—
111	C₂×D₃	—	25	1	no	—
112	C₂×C₅	—	3	6	no	—
113	D₅	—	5	6	no	—
114	D₅	—	15	6	no	—
115	C₃²	C₂×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
116	C₂×C₃	—	3	1	no	—
117	C₂×C₃	—	25	1	no	—
118	C₂×C₃	—	25	1	no	—
119	C₂×C₃	—	50	1	no	—
120	C₂×C₃	—	75	1	no	—
121	D₃	—	25	1	no	—
122	D₃	C₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
123	C₅	C₃×D₃×D₅×C₁₉	1	6	yes	complemented
124	C₂²	—	75	1	no	Sylow
125	C₃	—	2	1	no	—
126	C₃	D₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, direct product factor
127	C₃	C₂×C₃×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented
128	C₂	—	3	1	no	—
129	C₂	—	25	1	no	—
130	C₂	—	75	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₁₉×C₃⋊(C₅⋊D₅)

C₂

yes

maximal, characteristic, complemented

C₃×C₅²×D₃×C₁₉

C₂

yes

maximal, characteristic, complemented

C₃²×C₁₉×C₅⋊D₅

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₁₉×C₅⋊D₅

—

maximal

D₃×C₁₉×C₅⋊D₅

C₃

yes

maximal, characteristic, direct product factor

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₃×D₃×D₅×C₁₉

—

maximal

C₁₉×C₃⋊(C₅⋊D₅)

C₂×C₃

yes

characteristic, complemented

C₅²×D₃×C₁₉

C₂×C₃

yes

characteristic, complemented

C₃×C₁₉×C₅⋊D₅

—

C₃×C₁₉×C₅⋊D₅

—

C₃×C₁₉×C₅⋊D₅

D₃

yes

characteristic, direct product factor

C₃×C₁₉×C₅⋊D₅

C₂×C₃

yes

characteristic, complemented

C₂×C₃×C₅²×C₁₉

—

C₂×C₁₉×C₅⋊D₅

—

Hall

C₃×C₁₉×D₁₅

—

C₃×C₅×D₃×C₁₉

D₅

yes

complemented

C₃²×D₅×C₁₉

—

C₃×C₅²×C₁₉

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₂×C₃×D₅×C₁₉

—

D₃×D₅×C₁₉

—

C₂×C₅²×C₁₉

—

C₁₉×C₅⋊D₅

—

C₁₉×C₅⋊D₅

C₃×D₃

yes

characteristic, direct product factor

C₃×D₃×C₅⋊D₅

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₅×C₁₉

C₂×D₅

yes

complemented

C₂×C₃×D₃×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉

—

C₁₉×D₁₅

—

C₅×D₃×C₁₉

C₃×D₅

yes

complemented

C₃×D₅×C₁₉

—

C₃×D₅×C₁₉

—

C₃×D₅×C₁₉

—

C₃×D₅×C₁₉

—

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₃×C₃⋊(C₅⋊D₅)

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅²×D₃

C₂×C₁₉

yes

characteristic, complemented

C₃²×C₅⋊D₅

C₂×C₁₉

yes

characteristic, complemented

C₂×D₅×C₁₉

—

C₂×C₃²×C₁₉

—

C₃×D₃×C₁₉

—

C₃×D₃×C₁₉

C₅⋊D₅

yes

characteristic, direct product factor

C₂×C₃×C₅⋊D₅

—

D₃×C₅⋊D₅

C₃×C₁₉

yes

characteristic, direct product factor

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

D₃×D₅

yes

complemented

C₃×C₅×C₁₉

C₂×C₃×D₅

yes

complemented

C₂²×C₃×C₁₉

—

C₂×D₃×C₁₉

—

C₃²×C₅²

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

D₅×C₁₉

—

D₅×C₁₉

—

C₃×D₃×D₅

—

C₃²×C₁₉

C₂×C₅⋊D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₃⋊(C₅⋊D₅)

C₂×C₃×C₁₉

yes

characteristic, complemented

C₅²×D₃

C₂×C₃×C₁₉

yes

characteristic, complemented

C₃×C₅⋊D₅

—

C₃×C₅⋊D₅

—

C₃×C₅⋊D₅

D₃×C₁₉

yes

characteristic, direct product factor

C₃×C₅⋊D₅

C₂×C₃×C₁₉

yes

characteristic, complemented

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

D₃×C₁₉

—

D₃×C₁₉

C₃×C₅⋊D₅

yes

characteristic, direct product factor

C₂×C₅⋊D₅

—

Hall

C₅×C₁₉

C₃×D₃×D₅

yes

complemented

C₃×D₁₅

—

C₃×C₅×D₃

D₅×C₁₉

yes

complemented

C₃²×D₅

—

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

C₂×D₃×C₁₉

yes

characteristic, complemented

C₃×C₅²

C₂²×C₃×C₁₉

yes

characteristic, complemented

C₂×C₃×D₅

—

D₃×D₅

—

C₃×C₁₉

—

C₃×C₁₉

D₃×C₅⋊D₅

yes

characteristic, direct product factor

C₃×C₁₉

C₂×C₃×C₅⋊D₅

yes

characteristic, complemented

C₂×C₅²

—

C₅⋊D₅

—

C₅⋊D₅

C₃×D₃×C₁₉

yes

characteristic, direct product factor

C₃²×C₅

C₂×D₅×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₃×D₃

—

Hall

C₂×C₃×C₅

—

D₁₅

—

C₃×D₅

—

C₃×D₅

—

C₃×D₅

—

C₃×D₅

—

100

C₅×D₃

C₃×D₅×C₁₉

yes

complemented

101

C₅²

C₂×C₃×D₃×C₁₉

yes

characteristic, complemented, Sylow

102

C₂×D₅

—

103

C₁₉

C₃×D₃×C₅⋊D₅

yes

characteristic, direct product factor, Sylow

104

C₂×C₃²

—

105

C₃×D₃

—

106

C₃×D₃

C₁₉×C₅⋊D₅

yes

characteristic, direct product factor

107

C₃×C₅

—

108

C₃×C₅

D₃×D₅×C₁₉

yes

complemented

109

C₃×C₅

C₂×C₃×D₅×C₁₉

yes

complemented

110

C₂²×C₃

—

111

C₂×D₃

—

112

C₂×C₅

—

113

D₅

—

114

D₅

—

115

C₃²

C₂×C₁₉×C₅⋊D₅

yes

characteristic, complemented, Sylow

116

C₂×C₃

—

117

C₂×C₃

—

118

C₂×C₃

—

119

C₂×C₃

—

120

C₂×C₃

—

121

D₃

—

122

D₃

C₃×C₁₉×C₅⋊D₅

yes

characteristic, direct product factor

123

C₅

C₃×D₃×D₅×C₁₉

yes

complemented

124

C₂²

—

Sylow

125

C₃

—

126

C₃

D₃×C₁₉×C₅⋊D₅

yes

characteristic, direct product factor

127

C₃

C₂×C₃×C₁₉×C₅⋊D₅

yes

characteristic, complemented

128

C₂

—

129

C₂

—

130

C₂

—

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₃×C₅⋊D₅
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₃×C₁₉

subgroup

G/H

center, hypercenter

C₃×C₁₉

D₃×C₅⋊D₅

commutator, cosocle, hypocenter

C₃×C₅²

C₂²×C₃×C₁₉

Frattini

C₁

Fitting, socle

C₃²×C₅²×C₁₉

C₂²

LCS

G ▷ C₃×C₅²

UCS

C₁ ◁ C₃×C₁₉

N	H ≅ G/N	type
1. C₃×C₁₉×C₃⋊(C₅⋊D₅)	C₂	semidirect
2. C₃×C₅²×D₃×C₁₉	C₂	semidirect
3. C₃²×C₁₉×C₅⋊D₅	C₂	semidirect
5. D₃×C₁₉×C₅⋊D₅	C₃	direct (N × H)
6. C₃²×C₅²×C₁₉	C₂²	semidirect
8. C₁₉×C₃⋊(C₅⋊D₅)	C₂×C₃	semidirect
9. C₅²×D₃×C₁₉	C₂×C₃	semidirect
12. C₃×C₁₉×C₅⋊D₅	D₃	direct (N × H)
13. C₃×C₁₉×C₅⋊D₅	C₂×C₃	semidirect
17. C₃×C₅×D₃×C₁₉	D₅	semidirect
20. C₃×C₅²×C₁₉	C₂×D₃	semidirect
21. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
26. C₁₉×C₅⋊D₅	C₃×D₃	direct (N × H)
27. C₃×D₃×C₅⋊D₅	C₁₉	direct (N × H)
28. C₃²×C₅×C₁₉	C₂×D₅	semidirect
32. C₅×D₃×C₁₉	C₃×D₅	semidirect
37. C₅²×C₁₉	C₂×C₃×D₃	semidirect
38. C₃×C₃⋊(C₅⋊D₅)	C₂×C₁₉	semidirect
39. C₃×C₅²×D₃	C₂×C₁₉	semidirect
40. C₃²×C₅⋊D₅	C₂×C₁₉	semidirect
44. C₃×D₃×C₁₉	C₅⋊D₅	direct (N × H)
46. D₃×C₅⋊D₅	C₃×C₁₉	direct (N × H)
48. C₃×C₅×C₁₉	D₃×D₅	semidirect
49. C₃×C₅×C₁₉	C₂×C₃×D₅	semidirect
52. C₃²×C₅²	C₂²×C₁₉	semidirect
57. C₃²×C₁₉	C₂×C₅⋊D₅	semidirect
59. C₃⋊(C₅⋊D₅)	C₂×C₃×C₁₉	semidirect
60. C₅²×D₃	C₂×C₃×C₁₉	semidirect
63. C₃×C₅⋊D₅	D₃×C₁₉	direct (N × H)
64. C₃×C₅⋊D₅	C₂×C₃×C₁₉	semidirect
71. D₃×C₁₉	C₃×C₅⋊D₅	direct (N × H)
73. C₅×C₁₉	C₃×D₃×D₅	semidirect
75. C₃×C₅×D₃	D₅×C₁₉	semidirect
79. C₃×C₅²	C₂×D₃×C₁₉	semidirect
80. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
84. C₃×C₁₉	D₃×C₅⋊D₅	direct (N × H)
85. C₃×C₁₉	C₂×C₃×C₅⋊D₅	semidirect
88. C₅⋊D₅	C₃×D₃×C₁₉	direct (N × H)
89. C₃²×C₅	C₂×D₅×C₁₉	semidirect
100. C₅×D₃	C₃×D₅×C₁₉	semidirect
101. C₅²	C₂×C₃×D₃×C₁₉	semidirect
103. C₁₉	C₃×D₃×C₅⋊D₅	direct (N × H)
106. C₃×D₃	C₁₉×C₅⋊D₅	direct (N × H)
108. C₃×C₅	D₃×D₅×C₁₉	semidirect
109. C₃×C₅	C₂×C₃×D₅×C₁₉	semidirect
115. C₃²	C₂×C₁₉×C₅⋊D₅	semidirect
122. D₃	C₃×C₁₉×C₅⋊D₅	direct (N × H)
123. C₅	C₃×D₃×D₅×C₁₉	semidirect
126. C₃	D₃×C₁₉×C₅⋊D₅	direct (N × H)
127. C₃	C₂×C₃×C₁₉×C₅⋊D₅	semidirect

H ≅ G/N

type

1. C₃×C₁₉×C₃⋊(C₅⋊D₅)

C₂

semidirect

2. C₃×C₅²×D₃×C₁₉

C₂

semidirect

3. C₃²×C₁₉×C₅⋊D₅

C₂

semidirect

5. D₃×C₁₉×C₅⋊D₅

C₃

direct (N × H)

6. C₃²×C₅²×C₁₉

C₂²

semidirect

8. C₁₉×C₃⋊(C₅⋊D₅)

C₂×C₃

semidirect

9. C₅²×D₃×C₁₉

C₂×C₃

semidirect

12. C₃×C₁₉×C₅⋊D₅

D₃

direct (N × H)

13. C₃×C₁₉×C₅⋊D₅

C₂×C₃

semidirect

17. C₃×C₅×D₃×C₁₉

D₅

semidirect

20. C₃×C₅²×C₁₉

C₂×D₃

semidirect

21. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

26. C₁₉×C₅⋊D₅

C₃×D₃

direct (N × H)

27. C₃×D₃×C₅⋊D₅

C₁₉

direct (N × H)

28. C₃²×C₅×C₁₉

C₂×D₅

semidirect

32. C₅×D₃×C₁₉

C₃×D₅

semidirect

37. C₅²×C₁₉

C₂×C₃×D₃

semidirect

38. C₃×C₃⋊(C₅⋊D₅)

C₂×C₁₉

semidirect

39. C₃×C₅²×D₃

C₂×C₁₉

semidirect

40. C₃²×C₅⋊D₅

C₂×C₁₉

semidirect

44. C₃×D₃×C₁₉

C₅⋊D₅

direct (N × H)

46. D₃×C₅⋊D₅

C₃×C₁₉

direct (N × H)

48. C₃×C₅×C₁₉

D₃×D₅

semidirect

49. C₃×C₅×C₁₉

C₂×C₃×D₅

semidirect

52. C₃²×C₅²

C₂²×C₁₉

semidirect

57. C₃²×C₁₉

C₂×C₅⋊D₅

semidirect

59. C₃⋊(C₅⋊D₅)

C₂×C₃×C₁₉

semidirect

60. C₅²×D₃

C₂×C₃×C₁₉

semidirect

63. C₃×C₅⋊D₅

D₃×C₁₉

direct (N × H)

64. C₃×C₅⋊D₅

C₂×C₃×C₁₉

semidirect

71. D₃×C₁₉

C₃×C₅⋊D₅

direct (N × H)

73. C₅×C₁₉

C₃×D₃×D₅

semidirect

75. C₃×C₅×D₃

D₅×C₁₉

semidirect

79. C₃×C₅²

C₂×D₃×C₁₉

semidirect

80. C₃×C₅²

C₂²×C₃×C₁₉

semidirect

84. C₃×C₁₉

D₃×C₅⋊D₅

direct (N × H)

85. C₃×C₁₉

C₂×C₃×C₅⋊D₅

semidirect

88. C₅⋊D₅

C₃×D₃×C₁₉

direct (N × H)

89. C₃²×C₅

C₂×D₅×C₁₉

semidirect

100. C₅×D₃

C₃×D₅×C₁₉

semidirect

101. C₅²

C₂×C₃×D₃×C₁₉

semidirect

103. C₁₉

C₃×D₃×C₅⋊D₅

direct (N × H)

106. C₃×D₃

C₁₉×C₅⋊D₅

direct (N × H)

108. C₃×C₅

D₃×D₅×C₁₉

semidirect

109. C₃×C₅

C₂×C₃×D₅×C₁₉

semidirect

115. C₃²

C₂×C₁₉×C₅⋊D₅

semidirect

122. D₃

C₃×C₁₉×C₅⋊D₅

direct (N × H)

123. C₅

C₃×D₃×D₅×C₁₉

semidirect

126. C₃

D₃×C₁₉×C₅⋊D₅

direct (N × H)

127. C₃

C₂×C₃×C₁₉×C₅⋊D₅

semidirect

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

subgroup	index
C₃×C₁₉×C₃⋊(C₅⋊D₅)	2
C₃×C₅²×D₃×C₁₉	2
C₃²×C₁₉×C₅⋊D₅	2
C₂×C₃×C₁₉×C₅⋊D₅	3
D₃×C₁₉×C₅⋊D₅	3
C₃×D₃×D₅×C₁₉	5
C₃×D₃×C₅⋊D₅	19

subgroup

index

C₃×C₁₉×C₃⋊(C₅⋊D₅)

C₃×C₅²×D₃×C₁₉

C₃²×C₁₉×C₅⋊D₅

C₂×C₃×C₁₉×C₅⋊D₅

D₃×C₁₉×C₅⋊D₅

C₃×D₃×D₅×C₁₉

C₃×D₃×C₅⋊D₅

Subgroups — C₃×D₃×C₁₉×C₅⋊D₅ #30685883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×D3×C19×C5⋊D5 #30685883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×C₁₉×C₅⋊D₅ #30685883