Group #44478294 — subgroups

Subgroups — C₅×C₁₃×C₃⋊D₃×D₁₃ #44478294

Order 30420.

384 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 88 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	C₃²×C₅×C₁₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₁₃×D₁₃	—	3	4	no	maximal
5	C₃²×C₅×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃×C₃⋊D₃×D₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×D₃₉	—	3	4	no	—
8	C₅×D₃×C₁₃²	—	3	4	no	—
9	C₃×C₅×C₁₃×D₁₃	D₃	1	4	yes	complemented
10	C₂×C₅×C₁₃×D₁₃	—	9	1	no	Hall
11	C₁₃×C₃⋊D₃₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₁₃²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
13	C₃²×C₁₃×D₁₃	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₃²	C₂×D₃	1	4	yes	complemented
15	C₂×C₅×C₁₃×C₃⋊D₃	—	13	1	no	maximal
16	C₅×C₃⋊D₃×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
17	D₃×C₁₃×D₁₃	—	3	4	no	—
18	C₂×C₅×C₁₃²	—	9	1	no	—
19	C₅×C₁₃×D₁₃	—	9	1	no	—
20	C₅×C₁₃×D₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
21	C₃²×C₁₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₅×C₁₃	—	13	1	no	—
23	C₅×C₃⋊D₃₉	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₅×C₁₃×C₃⋊D₃	—	2	6	no	—
25	C₅×C₁₃×C₃⋊D₃	—	13	1	no	—
26	C₅×C₁₃×C₃⋊D₃	D₁₃	1	1	yes	characteristic, direct product factor
27	C₅×C₁₃×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic, complemented
28	C₃²×C₅×D₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
29	C₁₃×D₃₉	—	3	4	no	—
30	D₃×C₁₃²	—	3	4	no	—
31	C₃×C₁₃×D₁₃	C₅×D₃	1	4	yes	complemented
32	C₅×C₁₃²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₅×D₃×C₁₃	—	39	4	no	—
34	C₅×D₃×D₁₃	—	3	4	no	—
35	C₂×C₁₃×D₁₃	—	9	1	no	Hall
36	C₃²×C₅×C₁₃	—	2	6	no	—
37	C₃²×C₅×C₁₃	C₂×D₁₃	1	1	yes	characteristic, complemented
38	C₃²×C₅×C₁₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
39	C₃×C₁₃²	C₂×C₅×D₃	1	4	yes	complemented
40	C₂×C₁₃×C₃⋊D₃	—	13	1	no	—
41	C₃⋊D₃×D₁₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor
42	C₂×C₃×C₅×C₁₃	—	13	4	no	—
43	C₅×D₃₉	—	3	4	no	—
44	C₅×D₃×C₁₃	—	3	4	no	—
45	C₅×D₃×C₁₃	—	3	4	no	—
46	C₅×D₃×C₁₃	—	6	24	no	—
47	C₅×D₃×C₁₃	—	39	4	no	—
48	C₃×C₅×D₁₃	D₃×C₁₃	1	4	yes	complemented
49	C₂×C₁₃²	—	9	1	no	—
50	C₁₃×D₁₃	—	9	1	no	—
51	C₁₃×D₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
52	C₂²×C₅×C₁₃	—	117	1	no	—
53	C₂×C₅×D₁₃	—	9	1	no	—
54	C₂×C₃²×C₁₃	—	13	1	no	—
55	C₃⋊D₃₉	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
56	C₁₃×C₃⋊D₃	—	2	6	no	—
57	C₁₃×C₃⋊D₃	—	13	1	no	—
58	C₁₃×C₃⋊D₃	C₅×D₁₃	1	1	yes	characteristic, direct product factor
59	C₁₃×C₃⋊D₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
60	C₃²×D₁₃	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
61	C₃×C₅×C₁₃	—	2	24	no	—
62	C₃×C₅×C₁₃	D₃×D₁₃	1	4	yes	complemented
63	C₃×C₅×C₁₃	C₂×D₃×C₁₃	1	4	yes	complemented
64	C₂×C₅×C₃⋊D₃	—	13	1	no	Hall
65	C₁₃²	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×D₃×C₁₃	—	39	4	no	—
67	D₃×D₁₃	—	3	4	no	—
68	C₂×C₅×C₁₃	—	9	1	no	—
69	C₂×C₅×C₁₃	—	9	1	no	—
70	C₂×C₅×C₁₃	—	13	1	no	—
71	C₂×C₅×C₁₃	—	18	6	no	—
72	C₂×C₅×C₁₃	—	117	1	no	—
73	C₅×D₁₃	—	9	1	no	—
74	C₅×D₁₃	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
75	C₃²×C₁₃	—	2	6	no	—
76	C₃²×C₁₃	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented
77	C₃²×C₁₃	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented
78	C₂×C₃²×C₅	—	13	1	no	—
79	C₅×C₃⋊D₃	—	13	1	no	—
80	C₅×C₃⋊D₃	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
81	C₂×C₃×C₁₃	—	13	4	no	—
82	D₃₉	—	3	4	no	—
83	C₃×D₁₃	C₅×D₃×C₁₃	1	4	yes	complemented
84	D₃×C₁₃	—	3	4	no	—
85	D₃×C₁₃	—	3	4	no	—
86	D₃×C₁₃	—	6	24	no	—
87	D₃×C₁₃	—	39	4	no	—
88	C₅×C₁₃	—	2	6	no	—
89	C₅×C₁₃	C₃⋊D₃×D₁₃	1	1	yes	characteristic, direct product factor
90	C₅×C₁₃	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
91	C₂×C₅×D₃	—	39	4	no	—
92	C₂²×C₁₃	—	117	1	no	—
93	C₂×D₁₃	—	9	1	no	—
94	C₃²×C₅	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
95	C₃×C₁₃	—	2	24	no	—
96	C₃×C₁₃	C₅×D₃×D₁₃	1	4	yes	complemented
97	C₃×C₁₃	C₂×C₅×D₃×C₁₃	1	4	yes	complemented
98	C₂×C₃⋊D₃	—	13	1	no	Hall
99	C₂×C₃×C₅	—	13	4	no	—
100	C₅×D₃	—	3	4	no	—
101	C₅×D₃	—	39	4	no	—
102	C₂×C₁₃	—	9	1	no	—
103	C₂×C₁₃	—	9	1	no	—
104	C₂×C₁₃	—	13	1	no	—
105	C₂×C₁₃	—	18	6	no	—
106	C₂×C₁₃	—	117	1	no	—
107	D₁₃	—	9	1	no	—
108	D₁₃	C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
109	C₂²×C₅	—	117	1	no	Hall
110	C₂×C₃²	—	13	1	no	—
111	C₃⋊D₃	—	13	1	no	—
112	C₃⋊D₃	C₅×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
113	C₃×C₅	D₃×C₁₃×D₁₃	1	4	yes	complemented
114	C₁₃	—	2	6	no	—
115	C₁₃	C₅×C₃⋊D₃×D₁₃	1	1	yes	characteristic, direct product factor
116	C₁₃	C₂×C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, complemented
117	C₂×D₃	—	39	4	no	—
118	C₂×C₅	—	9	1	no	—
119	C₂×C₅	—	13	1	no	—
120	C₂×C₅	—	117	1	no	—
121	C₃²	C₂×C₅×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
122	C₂×C₃	—	13	4	no	—
123	D₃	—	3	4	no	—
124	D₃	—	39	4	no	—
125	C₅	C₁₃×C₃⋊D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²	—	117	1	no	Sylow
127	C₃	C₅×D₃×C₁₃×D₁₃	1	4	yes	complemented
128	C₂	—	9	1	no	—
129	C₂	—	13	1	no	—
130	C₂	—	117	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₅×C₁₃×D₁₃

C₂

yes

maximal, characteristic, complemented

C₅×C₁₃²×C₃⋊D₃

C₂

yes

maximal, characteristic, complemented

C₅×C₁₃×C₃⋊D₃₉

C₂

yes

maximal, characteristic, complemented

C₅×D₃×C₁₃×D₁₃

—

maximal

C₃²×C₅×C₁₃²

C₂²

yes

characteristic, complemented, Hall

C₁₃×C₃⋊D₃×D₁₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×C₁₃×D₃₉

—

C₅×D₃×C₁₃²

—

C₃×C₅×C₁₃×D₁₃

D₃

yes

complemented

C₂×C₅×C₁₃×D₁₃

—

Hall

C₁₃×C₃⋊D₃₉

C₂×C₅

yes

characteristic, complemented

C₁₃²×C₃⋊D₃

C₂×C₅

yes

characteristic, complemented

C₃²×C₁₃×D₁₃

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₁₃²

C₂×D₃

yes

complemented

C₂×C₅×C₁₃×C₃⋊D₃

—

maximal

C₅×C₃⋊D₃×D₁₃

C₁₃

yes

maximal, characteristic, direct product factor

D₃×C₁₃×D₁₃

—

C₂×C₅×C₁₃²

—

C₅×C₁₃×D₁₃

—

C₅×C₁₃×D₁₃

C₃⋊D₃

yes

characteristic, direct product factor

C₃²×C₁₃²

C₂²×C₅

yes

characteristic, complemented, Hall

C₂×C₃²×C₅×C₁₃

—

C₅×C₃⋊D₃₉

C₂×C₁₃

yes

characteristic, complemented

C₅×C₁₃×C₃⋊D₃

—

C₅×C₁₃×C₃⋊D₃

—

C₅×C₁₃×C₃⋊D₃

D₁₃

yes

characteristic, direct product factor

C₅×C₁₃×C₃⋊D₃

C₂×C₁₃

yes

characteristic, complemented

C₃²×C₅×D₁₃

C₂×C₁₃

yes

characteristic, complemented

C₁₃×D₃₉

—

D₃×C₁₃²

—

C₃×C₁₃×D₁₃

C₅×D₃

yes

complemented

C₅×C₁₃²

C₂×C₃⋊D₃

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₃

—

C₅×D₃×D₁₃

—

C₂×C₁₃×D₁₃

—

Hall

C₃²×C₅×C₁₃

—

C₃²×C₅×C₁₃

C₂×D₁₃

yes

characteristic, complemented

C₃²×C₅×C₁₃

C₂²×C₁₃

yes

characteristic, complemented

C₃×C₁₃²

C₂×C₅×D₃

yes

complemented

C₂×C₁₃×C₃⋊D₃

—

C₃⋊D₃×D₁₃

C₅×C₁₃

yes

characteristic, direct product factor

C₂×C₃×C₅×C₁₃

—

C₅×D₃₉

—

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

—

C₅×D₃×C₁₃

—

C₃×C₅×D₁₃

D₃×C₁₃

yes

complemented

C₂×C₁₃²

—

C₁₃×D₁₃

—

C₁₃×D₁₃

C₅×C₃⋊D₃

yes

characteristic, direct product factor

C₂²×C₅×C₁₃

—

117

—

C₂×C₅×D₁₃

—

C₂×C₃²×C₁₃

—

C₃⋊D₃₉

C₂×C₅×C₁₃

yes

characteristic, complemented

C₁₃×C₃⋊D₃

—

C₁₃×C₃⋊D₃

—

C₁₃×C₃⋊D₃

C₅×D₁₃

yes

characteristic, direct product factor

C₁₃×C₃⋊D₃

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃²×D₁₃

C₂×C₅×C₁₃

yes

characteristic, complemented

C₃×C₅×C₁₃

—

C₃×C₅×C₁₃

D₃×D₁₃

yes

complemented

C₃×C₅×C₁₃

C₂×D₃×C₁₃

yes

complemented

C₂×C₅×C₃⋊D₃

—

Hall

C₁₃²

C₂×C₅×C₃⋊D₃

yes

characteristic, complemented, Sylow

C₂×D₃×C₁₃

—

D₃×D₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

C₂×C₅×C₁₃

—

117

—

C₅×D₁₃

—

C₅×D₁₃

C₁₃×C₃⋊D₃

yes

characteristic, direct product factor

C₃²×C₁₃

—

C₃²×C₁₃

C₂×C₅×D₁₃

yes

characteristic, complemented

C₃²×C₁₃

C₂²×C₅×C₁₃

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₅×C₃⋊D₃

—

C₅×C₃⋊D₃

C₁₃×D₁₃

yes

characteristic, direct product factor

C₂×C₃×C₁₃

—

D₃₉

—

C₃×D₁₃

C₅×D₃×C₁₃

yes

complemented

D₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

—

D₃×C₁₃

—

C₅×C₁₃

—

C₅×C₁₃

C₃⋊D₃×D₁₃

yes

characteristic, direct product factor

C₅×C₁₃

C₂×C₁₃×C₃⋊D₃

yes

characteristic, complemented

C₂×C₅×D₃

—

C₂²×C₁₃

—

117

—

C₂×D₁₃

—

C₃²×C₅

C₂×C₁₃×D₁₃

yes

characteristic, complemented, Hall

C₃×C₁₃

—

C₃×C₁₃

C₅×D₃×D₁₃

yes

complemented

C₃×C₁₃

C₂×C₅×D₃×C₁₃

yes

complemented

C₂×C₃⋊D₃

—

Hall

C₂×C₃×C₅

—

100

C₅×D₃

—

101

C₅×D₃

—

102

C₂×C₁₃

—

103

C₂×C₁₃

—

104

C₂×C₁₃

—

105

C₂×C₁₃

—

106

C₂×C₁₃

—

117

—

107

D₁₃

—

108

D₁₃

C₅×C₁₃×C₃⋊D₃

yes

characteristic, direct product factor

109

C₂²×C₅

—

117

Hall

110

C₂×C₃²

—

111

C₃⋊D₃

—

112

C₃⋊D₃

C₅×C₁₃×D₁₃

yes

characteristic, direct product factor

113

C₃×C₅

D₃×C₁₃×D₁₃

yes

complemented

114

C₁₃

—

115

C₁₃

C₅×C₃⋊D₃×D₁₃

yes

characteristic, direct product factor

116

C₁₃

C₂×C₅×C₁₃×C₃⋊D₃

yes

characteristic, complemented

117

C₂×D₃

—

118

C₂×C₅

—

119

C₂×C₅

—

120

C₂×C₅

—

117

—

121

C₃²

C₂×C₅×C₁₃×D₁₃

yes

characteristic, complemented, Sylow

122

C₂×C₃

—

123

D₃

—

124

D₃

—

125

C₅

C₁₃×C₃⋊D₃×D₁₃

yes

characteristic, direct product factor, Sylow

126

C₂²

—

117

Sylow

127

C₃

C₅×D₃×C₁₃×D₁₃

yes

complemented

128

C₂

—

129

C₂

—

130

C₂

—

117

—

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₃⋊D₃×D₁₃
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃²	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₅×C₁₃

subgroup

G/H

center, hypercenter

C₅×C₁₃

C₃⋊D₃×D₁₃

commutator, cosocle, hypocenter

C₃²×C₁₃

C₂²×C₅×C₁₃

Frattini

C₁

Fitting, socle

C₃²×C₅×C₁₃²

C₂²

LCS

G ▷ C₃²×C₁₃

UCS

C₁ ◁ C₅×C₁₃

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×D₁₃	C₂	semidirect
2. C₅×C₁₃²×C₃⋊D₃	C₂	semidirect
3. C₅×C₁₃×C₃⋊D₃₉	C₂	semidirect
5. C₃²×C₅×C₁₃²	C₂²	semidirect
6. C₁₃×C₃⋊D₃×D₁₃	C₅	direct (N × H)
9. C₃×C₅×C₁₃×D₁₃	D₃	semidirect
11. C₁₃×C₃⋊D₃₉	C₂×C₅	semidirect
12. C₁₃²×C₃⋊D₃	C₂×C₅	semidirect
13. C₃²×C₁₃×D₁₃	C₂×C₅	semidirect
14. C₃×C₅×C₁₃²	C₂×D₃	semidirect
16. C₅×C₃⋊D₃×D₁₃	C₁₃	direct (N × H)
20. C₅×C₁₃×D₁₃	C₃⋊D₃	direct (N × H)
21. C₃²×C₁₃²	C₂²×C₅	semidirect
23. C₅×C₃⋊D₃₉	C₂×C₁₃	semidirect
26. C₅×C₁₃×C₃⋊D₃	D₁₃	direct (N × H)
27. C₅×C₁₃×C₃⋊D₃	C₂×C₁₃	semidirect
28. C₃²×C₅×D₁₃	C₂×C₁₃	semidirect
31. C₃×C₁₃×D₁₃	C₅×D₃	semidirect
32. C₅×C₁₃²	C₂×C₃⋊D₃	semidirect
37. C₃²×C₅×C₁₃	C₂×D₁₃	semidirect
38. C₃²×C₅×C₁₃	C₂²×C₁₃	semidirect
39. C₃×C₁₃²	C₂×C₅×D₃	semidirect
41. C₃⋊D₃×D₁₃	C₅×C₁₃	direct (N × H)
48. C₃×C₅×D₁₃	D₃×C₁₃	semidirect
51. C₁₃×D₁₃	C₅×C₃⋊D₃	direct (N × H)
55. C₃⋊D₃₉	C₂×C₅×C₁₃	semidirect
58. C₁₃×C₃⋊D₃	C₅×D₁₃	direct (N × H)
59. C₁₃×C₃⋊D₃	C₂×C₅×C₁₃	semidirect
60. C₃²×D₁₃	C₂×C₅×C₁₃	semidirect
62. C₃×C₅×C₁₃	D₃×D₁₃	semidirect
63. C₃×C₅×C₁₃	C₂×D₃×C₁₃	semidirect
65. C₁₃²	C₂×C₅×C₃⋊D₃	semidirect
74. C₅×D₁₃	C₁₃×C₃⋊D₃	direct (N × H)
76. C₃²×C₁₃	C₂×C₅×D₁₃	semidirect
77. C₃²×C₁₃	C₂²×C₅×C₁₃	semidirect
80. C₅×C₃⋊D₃	C₁₃×D₁₃	direct (N × H)
83. C₃×D₁₃	C₅×D₃×C₁₃	semidirect
89. C₅×C₁₃	C₃⋊D₃×D₁₃	direct (N × H)
90. C₅×C₁₃	C₂×C₁₃×C₃⋊D₃	semidirect
94. C₃²×C₅	C₂×C₁₃×D₁₃	semidirect
96. C₃×C₁₃	C₅×D₃×D₁₃	semidirect
97. C₃×C₁₃	C₂×C₅×D₃×C₁₃	semidirect
108. D₁₃	C₅×C₁₃×C₃⋊D₃	direct (N × H)
112. C₃⋊D₃	C₅×C₁₃×D₁₃	direct (N × H)
113. C₃×C₅	D₃×C₁₃×D₁₃	semidirect
115. C₁₃	C₅×C₃⋊D₃×D₁₃	direct (N × H)
116. C₁₃	C₂×C₅×C₁₃×C₃⋊D₃	semidirect
121. C₃²	C₂×C₅×C₁₃×D₁₃	semidirect
125. C₅	C₁₃×C₃⋊D₃×D₁₃	direct (N × H)
127. C₃	C₅×D₃×C₁₃×D₁₃	semidirect

H ≅ G/N

type

1. C₃²×C₅×C₁₃×D₁₃

C₂

semidirect

2. C₅×C₁₃²×C₃⋊D₃

C₂

semidirect

3. C₅×C₁₃×C₃⋊D₃₉

C₂

semidirect

5. C₃²×C₅×C₁₃²

C₂²

semidirect

6. C₁₃×C₃⋊D₃×D₁₃

C₅

direct (N × H)

9. C₃×C₅×C₁₃×D₁₃

D₃

semidirect

11. C₁₃×C₃⋊D₃₉

C₂×C₅

semidirect

12. C₁₃²×C₃⋊D₃

C₂×C₅

semidirect

13. C₃²×C₁₃×D₁₃

C₂×C₅

semidirect

14. C₃×C₅×C₁₃²

C₂×D₃

semidirect

16. C₅×C₃⋊D₃×D₁₃

C₁₃

direct (N × H)

20. C₅×C₁₃×D₁₃

C₃⋊D₃

direct (N × H)

21. C₃²×C₁₃²

C₂²×C₅

semidirect

23. C₅×C₃⋊D₃₉

C₂×C₁₃

semidirect

26. C₅×C₁₃×C₃⋊D₃

D₁₃

direct (N × H)

27. C₅×C₁₃×C₃⋊D₃

C₂×C₁₃

semidirect

28. C₃²×C₅×D₁₃

C₂×C₁₃

semidirect

31. C₃×C₁₃×D₁₃

C₅×D₃

semidirect

32. C₅×C₁₃²

C₂×C₃⋊D₃

semidirect

37. C₃²×C₅×C₁₃

C₂×D₁₃

semidirect

38. C₃²×C₅×C₁₃

C₂²×C₁₃

semidirect

39. C₃×C₁₃²

C₂×C₅×D₃

semidirect

41. C₃⋊D₃×D₁₃

C₅×C₁₃

direct (N × H)

48. C₃×C₅×D₁₃

D₃×C₁₃

semidirect

51. C₁₃×D₁₃

C₅×C₃⋊D₃

direct (N × H)

55. C₃⋊D₃₉

C₂×C₅×C₁₃

semidirect

58. C₁₃×C₃⋊D₃

C₅×D₁₃

direct (N × H)

59. C₁₃×C₃⋊D₃

C₂×C₅×C₁₃

semidirect

60. C₃²×D₁₃

C₂×C₅×C₁₃

semidirect

62. C₃×C₅×C₁₃

D₃×D₁₃

semidirect

63. C₃×C₅×C₁₃

C₂×D₃×C₁₃

semidirect

65. C₁₃²

C₂×C₅×C₃⋊D₃

semidirect

74. C₅×D₁₃

C₁₃×C₃⋊D₃

direct (N × H)

76. C₃²×C₁₃

C₂×C₅×D₁₃

semidirect

77. C₃²×C₁₃

C₂²×C₅×C₁₃

semidirect

80. C₅×C₃⋊D₃

C₁₃×D₁₃

direct (N × H)

83. C₃×D₁₃

C₅×D₃×C₁₃

semidirect

89. C₅×C₁₃

C₃⋊D₃×D₁₃

direct (N × H)

90. C₅×C₁₃

C₂×C₁₃×C₃⋊D₃

semidirect

94. C₃²×C₅

C₂×C₁₃×D₁₃

semidirect

96. C₃×C₁₃

C₅×D₃×D₁₃

semidirect

97. C₃×C₁₃

C₂×C₅×D₃×C₁₃

semidirect

108. D₁₃

C₅×C₁₃×C₃⋊D₃

direct (N × H)

112. C₃⋊D₃

C₅×C₁₃×D₁₃

direct (N × H)

113. C₃×C₅

D₃×C₁₃×D₁₃

semidirect

115. C₁₃

C₅×C₃⋊D₃×D₁₃

direct (N × H)

116. C₁₃

C₂×C₅×C₁₃×C₃⋊D₃

semidirect

121. C₃²

C₂×C₅×C₁₃×D₁₃

semidirect

125. C₅

C₁₃×C₃⋊D₃×D₁₃

direct (N × H)

127. C₃

C₅×D₃×C₁₃×D₁₃

semidirect

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

subgroup	index
C₃²×C₅×C₁₃×D₁₃	2
C₅×C₁₃²×C₃⋊D₃	2
C₅×C₁₃×C₃⋊D₃₉	2
C₅×D₃×C₁₃×D₁₃	3
C₁₃×C₃⋊D₃×D₁₃	5
C₂×C₅×C₁₃×C₃⋊D₃	13
C₅×C₃⋊D₃×D₁₃	13

subgroup

index

C₃²×C₅×C₁₃×D₁₃

C₅×C₁₃²×C₃⋊D₃

C₅×C₁₃×C₃⋊D₃₉

C₅×D₃×C₁₃×D₁₃

C₁₃×C₃⋊D₃×D₁₃

C₂×C₅×C₁₃×C₃⋊D₃

C₅×C₃⋊D₃×D₁₃

Subgroups — C₅×C₁₃×C₃⋊D₃×D₁₃ #44478294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×C13×C3⋊D3×D13 #44478294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₃×C₃⋊D₃×D₁₃ #44478294