Group #41031966 — subgroups

Subgroups — C₅²×D₇×D₃₉ #41031966

Order 27300.

320 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 128 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×C₅²×C₁₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×C₇×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×D₂₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×D₇×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₇×D₃₉	C₅	1	6	yes	maximal, direct product factor
7	C₅²×D₉₁	—	3	1	no	—
8	C₅²×C₁₃×D₇	D₃	1	1	yes	characteristic, complemented
9	C₅²×C₇×D₁₃	—	3	1	no	—
10	C₂×C₅²×D₃₉	—	7	1	no	maximal, Hall
11	C₅×D₂₇₃	C₂×C₅	1	6	yes	complemented
12	C₅×C₇×D₃₉	C₂×C₅	1	6	yes	complemented
13	C₃×C₅×C₁₃×D₇	C₂×C₅	1	6	yes	complemented
14	C₅²×C₇×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×D₃×D₇	—	13	1	no	maximal, Hall
16	C₂×C₃×C₅²×C₁₃	—	7	1	no	—
17	C₅²×D₃₉	—	7	1	no	—
18	C₅²×D₃₉	D₇	1	1	yes	characteristic, direct product factor
19	C₅×D₇×D₁₃	—	3	6	no	—
20	C₃×C₅×C₇×C₁₃	C₂²×C₅	1	6	yes	complemented
21	C₂×C₅²×D₁₃	—	21	1	no	Hall
22	D₇×D₃₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₅²×D₂₁	—	13	1	no	—
24	C₅²×D₃×C₇	—	13	1	no	—
25	C₃×C₅²×D₇	D₁₃	1	1	yes	characteristic, complemented
26	C₃×C₅²×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
27	C₅×D₉₁	—	3	6	no	—
28	C₅×C₁₃×D₇	C₅×D₃	1	6	yes	complemented
29	C₅×C₇×D₁₃	—	3	6	no	—
30	C₂×C₅×D₃₉	—	7	6	no	—
31	C₂×C₅²×D₇	—	39	1	no	Hall
32	C₂×C₅²×C₁₃	—	7	1	no	—
33	C₅²×D₁₃	—	3	1	no	—
34	C₅²×D₁₃	—	21	1	no	—
35	D₂₇₃	C₂×C₅²	1	1	yes	characteristic, complemented
36	C₇×D₃₉	C₂×C₅²	1	1	yes	characteristic, complemented
37	C₃×C₁₃×D₇	C₂×C₅²	1	1	yes	characteristic, complemented
38	C₃×C₅²×C₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₅×C₇×C₁₃	C₂×C₅×D₃	1	6	yes	complemented
40	C₅×D₃×D₇	—	13	6	no	—
41	C₂×C₃×C₅×C₁₃	—	7	6	no	—
42	C₅×D₃₉	—	7	6	no	—
43	C₅×D₃₉	C₅×D₇	1	6	yes	direct product factor
44	D₇×D₁₃	—	3	1	no	Hall
45	C₂×C₅²×C₇	—	39	1	no	—
46	C₅²×D₇	—	39	1	no	—
47	C₅²×D₇	D₃₉	1	1	yes	characteristic, direct product factor
48	C₅²×C₁₃	D₃×D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₅²×D₃	—	91	1	no	Hall
50	C₃×C₇×C₁₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×D₁₃	—	21	6	no	—
52	C₅×D₂₁	—	13	6	no	—
53	C₅×D₃×C₇	—	13	6	no	—
54	C₃×C₅×D₇	C₅×D₁₃	1	6	yes	complemented
55	C₃×C₅×C₁₃	C₂×C₅×D₇	1	6	yes	complemented
56	D₉₁	—	3	1	no	—
57	C₇×D₁₃	—	3	1	no	—
58	C₁₃×D₇	C₅²×D₃	1	1	yes	characteristic, complemented
59	C₅²×C₇	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
60	C₂×D₃₉	—	7	1	no	Hall
61	C₂×C₃×C₅²	—	7	1	no	—
62	C₅²×D₃	—	13	1	no	—
63	C₅²×D₃	—	91	1	no	—
64	C₂×C₅×D₇	—	39	6	no	—
65	C₂×C₅×C₁₃	—	7	6	no	—
66	C₅×D₁₃	—	3	6	no	—
67	C₅×D₁₃	—	21	6	no	—
68	C₃×C₅×C₇	C₂×C₅×D₁₃	1	6	yes	complemented
69	C₂²×C₅²	—	273	1	no	Hall
70	C₇×C₁₃	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Hall
71	D₃×D₇	—	13	1	no	Hall
72	C₂×C₃×C₁₃	—	7	1	no	—
73	D₃₉	—	7	1	no	—
74	D₃₉	C₅²×D₇	1	1	yes	characteristic, direct product factor
75	C₃×C₅²	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
76	C₂×C₅×C₇	—	39	6	no	—
77	C₅×D₇	—	39	6	no	—
78	C₅×D₇	C₅×D₃₉	1	6	yes	direct product factor
79	C₅×C₁₃	C₅×D₃×D₇	1	6	yes	complemented
80	C₂×C₅×D₃	—	91	6	no	—
81	C₂×D₁₃	—	21	1	no	Hall
82	C₂×C₅²	—	7	1	no	—
83	C₂×C₅²	—	273	1	no	—
84	C₂×C₅²	—	39	1	no	—
85	D₂₁	—	13	1	no	—
86	C₃×D₇	C₅²×D₁₃	1	1	yes	characteristic, complemented
87	D₃×C₇	—	13	1	no	—
88	C₃×C₁₃	C₂×C₅²×D₇	1	1	yes	characteristic, complemented, Hall
89	C₅×C₇	C₂×C₅×D₃₉	1	6	yes	complemented
90	C₂×C₃×C₅	—	7	6	no	—
91	C₅×D₃	—	13	6	no	—
92	C₅×D₃	—	91	6	no	—
93	C₂×D₇	—	39	1	no	Hall
94	C₂×C₁₃	—	7	1	no	—
95	D₁₃	—	3	1	no	—
96	D₁₃	—	21	1	no	—
97	C₅²	D₇×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
98	C₃×C₇	C₂×C₅²×D₁₃	1	1	yes	characteristic, complemented, Hall
99	C₂²×C₅	—	273	6	no	—
100	C₃×C₅	C₅×D₇×D₁₃	1	6	yes	complemented
101	C₂×C₇	—	39	1	no	—
102	D₇	—	39	1	no	—
103	D₇	C₅²×D₃₉	1	1	yes	characteristic, direct product factor
104	C₁₃	C₅²×D₃×D₇	1	1	yes	characteristic, complemented, Sylow
105	C₂×D₃	—	91	1	no	Hall
106	C₂×C₅	—	7	6	no	—
107	C₂×C₅	—	273	6	no	—
108	C₂×C₅	—	39	6	no	—
109	C₇	C₂×C₅²×D₃₉	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	7	1	no	—
111	D₃	—	13	1	no	—
112	D₃	—	91	1	no	—
113	C₅	C₅×D₇×D₃₉	1	6	yes	direct product factor
114	C₂²	—	273	1	no	Sylow
115	C₃	C₅²×D₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
116	C₂	—	7	1	no	—
117	C₂	—	273	1	no	—
118	C₂	—	39	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅²×C₁₃×D₇

C₂

yes

maximal, characteristic, complemented

C₅²×C₇×D₃₉

C₂

yes

maximal, characteristic, complemented

C₅²×D₂₇₃

C₂

yes

maximal, characteristic, complemented

C₅²×D₇×D₁₃

—

maximal, Hall

C₃×C₅²×C₇×C₁₃

C₂²

yes

characteristic, complemented, Hall

C₅×D₇×D₃₉

C₅

yes

maximal, direct product factor

C₅²×D₉₁

—

C₅²×C₁₃×D₇

D₃

yes

characteristic, complemented

C₅²×C₇×D₁₃

—

C₂×C₅²×D₃₉

—

maximal, Hall

C₅×D₂₇₃

C₂×C₅

yes

complemented

C₅×C₇×D₃₉

C₂×C₅

yes

complemented

C₃×C₅×C₁₃×D₇

C₂×C₅

yes

complemented

C₅²×C₇×C₁₃

C₂×D₃

yes

characteristic, complemented, Hall

C₅²×D₃×D₇

—

maximal, Hall

C₂×C₃×C₅²×C₁₃

—

C₅²×D₃₉

—

C₅²×D₃₉

D₇

yes

characteristic, direct product factor

C₅×D₇×D₁₃

—

C₃×C₅×C₇×C₁₃

C₂²×C₅

yes

complemented

C₂×C₅²×D₁₃

—

Hall

D₇×D₃₉

C₅²

yes

characteristic, direct product factor, Hall

C₅²×D₂₁

—

C₅²×D₃×C₇

—

C₃×C₅²×D₇

D₁₃

yes

characteristic, complemented

C₃×C₅²×C₁₃

C₂×D₇

yes

characteristic, complemented, Hall

C₅×D₉₁

—

C₅×C₁₃×D₇

C₅×D₃

yes

complemented

C₅×C₇×D₁₃

—

C₂×C₅×D₃₉

—

C₂×C₅²×D₇

—

Hall

C₂×C₅²×C₁₃

—

C₅²×D₁₃

—

C₅²×D₁₃

—

D₂₇₃

C₂×C₅²

yes

characteristic, complemented

C₇×D₃₉

C₂×C₅²

yes

characteristic, complemented

C₃×C₁₃×D₇

C₂×C₅²

yes

characteristic, complemented

C₃×C₅²×C₇

C₂×D₁₃

yes

characteristic, complemented, Hall

C₅×C₇×C₁₃

C₂×C₅×D₃

yes

complemented

C₅×D₃×D₇

—

C₂×C₃×C₅×C₁₃

—

C₅×D₃₉

—

C₅×D₃₉

C₅×D₇

yes

direct product factor

D₇×D₁₃

—

Hall

C₂×C₅²×C₇

—

C₅²×D₇

—

C₅²×D₇

D₃₉

yes

characteristic, direct product factor

C₅²×C₁₃

D₃×D₇

yes

characteristic, complemented, Hall

C₂×C₅²×D₃

—

Hall

C₃×C₇×C₁₃

C₂²×C₅²

yes

characteristic, complemented, Hall

C₂×C₅×D₁₃

—

C₅×D₂₁

—

C₅×D₃×C₇

—

C₃×C₅×D₇

C₅×D₁₃

yes

complemented

C₃×C₅×C₁₃

C₂×C₅×D₇

yes

complemented

D₉₁

—

C₇×D₁₃

—

C₁₃×D₇

C₅²×D₃

yes

characteristic, complemented

C₅²×C₇

C₂×D₃₉

yes

characteristic, complemented, Hall

C₂×D₃₉

—

Hall

C₂×C₃×C₅²

—

C₅²×D₃

—

C₅²×D₃

—

C₂×C₅×D₇

—

C₂×C₅×C₁₃

—

C₅×D₁₃

—

C₅×D₁₃

—

C₃×C₅×C₇

C₂×C₅×D₁₃

yes

complemented

C₂²×C₅²

—

273

Hall

C₇×C₁₃

C₂×C₅²×D₃

yes

characteristic, complemented, Hall

D₃×D₇

—

Hall

C₂×C₃×C₁₃

—

D₃₉

—

D₃₉

C₅²×D₇

yes

characteristic, direct product factor

C₃×C₅²

D₇×D₁₃

yes

characteristic, complemented, Hall

C₂×C₅×C₇

—

C₅×D₇

—

C₅×D₇

C₅×D₃₉

yes

direct product factor

C₅×C₁₃

C₅×D₃×D₇

yes

complemented

C₂×C₅×D₃

—

C₂×D₁₃

—

Hall

C₂×C₅²

—

C₂×C₅²

—

273

—

C₂×C₅²

—

D₂₁

—

C₃×D₇

C₅²×D₁₃

yes

characteristic, complemented

D₃×C₇

—

C₃×C₁₃

C₂×C₅²×D₇

yes

characteristic, complemented, Hall

C₅×C₇

C₂×C₅×D₃₉

yes

complemented

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

—

C₂×D₇

—

Hall

C₂×C₁₃

—

D₁₃

—

D₁₃

—

C₅²

D₇×D₃₉

yes

characteristic, direct product factor, Sylow

C₃×C₇

C₂×C₅²×D₁₃

yes

characteristic, complemented, Hall

C₂²×C₅

—

273

—

100

C₃×C₅

C₅×D₇×D₁₃

yes

complemented

101

C₂×C₇

—

102

D₇

—

103

D₇

C₅²×D₃₉

yes

characteristic, direct product factor

104

C₁₃

C₅²×D₃×D₇

yes

characteristic, complemented, Sylow

105

C₂×D₃

—

Hall

106

C₂×C₅

—

107

C₂×C₅

—

273

—

108

C₂×C₅

—

109

C₇

C₂×C₅²×D₃₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

—

113

C₅

C₅×D₇×D₃₉

yes

direct product factor

114

C₂²

—

273

Sylow

115

C₃

C₅²×D₇×D₁₃

yes

characteristic, complemented, Sylow

116

C₂

—

117

C₂

—

273

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₅²	D₇×D₃₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₃	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₅²

subgroup

G/H

center, hypercenter

C₅²

D₇×D₃₉

commutator, cosocle, hypocenter

C₃×C₇×C₁₃

C₂²×C₅²

Frattini

C₁

Fitting, socle

C₃×C₅²×C₇×C₁₃

C₂²

LCS

G ▷ C₃×C₇×C₁₃

UCS

C₁ ◁ C₅²

N	H ≅ G/N	type
1. C₃×C₅²×C₁₃×D₇	C₂	semidirect
2. C₅²×C₇×D₃₉	C₂	semidirect
3. C₅²×D₂₇₃	C₂	semidirect
5. C₃×C₅²×C₇×C₁₃	C₂²	semidirect
6. C₅×D₇×D₃₉	C₅	direct (N × H)
8. C₅²×C₁₃×D₇	D₃	semidirect
11. C₅×D₂₇₃	C₂×C₅	semidirect
12. C₅×C₇×D₃₉	C₂×C₅	semidirect
13. C₃×C₅×C₁₃×D₇	C₂×C₅	semidirect
14. C₅²×C₇×C₁₃	C₂×D₃	semidirect
18. C₅²×D₃₉	D₇	direct (N × H)
20. C₃×C₅×C₇×C₁₃	C₂²×C₅	semidirect
22. D₇×D₃₉	C₅²	direct (N × H)
25. C₃×C₅²×D₇	D₁₃	semidirect
26. C₃×C₅²×C₁₃	C₂×D₇	semidirect
28. C₅×C₁₃×D₇	C₅×D₃	semidirect
35. D₂₇₃	C₂×C₅²	semidirect
36. C₇×D₃₉	C₂×C₅²	semidirect
37. C₃×C₁₃×D₇	C₂×C₅²	semidirect
38. C₃×C₅²×C₇	C₂×D₁₃	semidirect
39. C₅×C₇×C₁₃	C₂×C₅×D₃	semidirect
43. C₅×D₃₉	C₅×D₇	direct (N × H)
47. C₅²×D₇	D₃₉	direct (N × H)
48. C₅²×C₁₃	D₃×D₇	semidirect
50. C₃×C₇×C₁₃	C₂²×C₅²	semidirect
54. C₃×C₅×D₇	C₅×D₁₃	semidirect
55. C₃×C₅×C₁₃	C₂×C₅×D₇	semidirect
58. C₁₃×D₇	C₅²×D₃	semidirect
59. C₅²×C₇	C₂×D₃₉	semidirect
68. C₃×C₅×C₇	C₂×C₅×D₁₃	semidirect
70. C₇×C₁₃	C₂×C₅²×D₃	semidirect
74. D₃₉	C₅²×D₇	direct (N × H)
75. C₃×C₅²	D₇×D₁₃	semidirect
78. C₅×D₇	C₅×D₃₉	direct (N × H)
79. C₅×C₁₃	C₅×D₃×D₇	semidirect
86. C₃×D₇	C₅²×D₁₃	semidirect
88. C₃×C₁₃	C₂×C₅²×D₇	semidirect
89. C₅×C₇	C₂×C₅×D₃₉	semidirect
97. C₅²	D₇×D₃₉	direct (N × H)
98. C₃×C₇	C₂×C₅²×D₁₃	semidirect
100. C₃×C₅	C₅×D₇×D₁₃	semidirect
103. D₇	C₅²×D₃₉	direct (N × H)
104. C₁₃	C₅²×D₃×D₇	semidirect
109. C₇	C₂×C₅²×D₃₉	semidirect
113. C₅	C₅×D₇×D₃₉	direct (N × H)
115. C₃	C₅²×D₇×D₁₃	semidirect

H ≅ G/N

type

1. C₃×C₅²×C₁₃×D₇

C₂

semidirect

2. C₅²×C₇×D₃₉

C₂

semidirect

3. C₅²×D₂₇₃

C₂

semidirect

5. C₃×C₅²×C₇×C₁₃

C₂²

semidirect

6. C₅×D₇×D₃₉

C₅

direct (N × H)

8. C₅²×C₁₃×D₇

D₃

semidirect

11. C₅×D₂₇₃

C₂×C₅

semidirect

12. C₅×C₇×D₃₉

C₂×C₅

semidirect

13. C₃×C₅×C₁₃×D₇

C₂×C₅

semidirect

14. C₅²×C₇×C₁₃

C₂×D₃

semidirect

18. C₅²×D₃₉

D₇

direct (N × H)

20. C₃×C₅×C₇×C₁₃

C₂²×C₅

semidirect

22. D₇×D₃₉

C₅²

direct (N × H)

25. C₃×C₅²×D₇

D₁₃

semidirect

26. C₃×C₅²×C₁₃

C₂×D₇

semidirect

28. C₅×C₁₃×D₇

C₅×D₃

semidirect

35. D₂₇₃

C₂×C₅²

semidirect

36. C₇×D₃₉

C₂×C₅²

semidirect

37. C₃×C₁₃×D₇

C₂×C₅²

semidirect

38. C₃×C₅²×C₇

C₂×D₁₃

semidirect

39. C₅×C₇×C₁₃

C₂×C₅×D₃

semidirect

43. C₅×D₃₉

C₅×D₇

direct (N × H)

47. C₅²×D₇

D₃₉

direct (N × H)

48. C₅²×C₁₃

D₃×D₇

semidirect

50. C₃×C₇×C₁₃

C₂²×C₅²

semidirect

54. C₃×C₅×D₇

C₅×D₁₃

semidirect

55. C₃×C₅×C₁₃

C₂×C₅×D₇

semidirect

58. C₁₃×D₇

C₅²×D₃

semidirect

59. C₅²×C₇

C₂×D₃₉

semidirect

68. C₃×C₅×C₇

C₂×C₅×D₁₃

semidirect

70. C₇×C₁₃

C₂×C₅²×D₃

semidirect

74. D₃₉

C₅²×D₇

direct (N × H)

75. C₃×C₅²

D₇×D₁₃

semidirect

78. C₅×D₇

C₅×D₃₉

direct (N × H)

79. C₅×C₁₃

C₅×D₃×D₇

semidirect

86. C₃×D₇

C₅²×D₁₃

semidirect

88. C₃×C₁₃

C₂×C₅²×D₇

semidirect

89. C₅×C₇

C₂×C₅×D₃₉

semidirect

97. C₅²

D₇×D₃₉

direct (N × H)

98. C₃×C₇

C₂×C₅²×D₁₃

semidirect

100. C₃×C₅

C₅×D₇×D₁₃

semidirect

103. D₇

C₅²×D₃₉

direct (N × H)

104. C₁₃

C₅²×D₃×D₇

semidirect

109. C₇

C₂×C₅²×D₃₉

semidirect

113. C₅

C₅×D₇×D₃₉

direct (N × H)

115. C₃

C₅²×D₇×D₁₃

semidirect

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

subgroup	index
C₃×C₅²×C₁₃×D₇	2
C₅²×C₇×D₃₉	2
C₅²×D₂₇₃	2
C₅²×D₇×D₁₃	3
C₅×D₇×D₃₉	5
C₂×C₅²×D₃₉	7
C₅²×D₃×D₇	13

subgroup

index

C₃×C₅²×C₁₃×D₇

C₅²×C₇×D₃₉

C₅²×D₂₇₃

C₅²×D₇×D₁₃

C₅×D₇×D₃₉

C₂×C₅²×D₃₉

C₅²×D₃×D₇

Subgroups — C₅²×D₇×D₃₉ #41031966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C52×D7×D39 #41031966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₇×D₃₉ #41031966