Group #30685975 — subgroups

Subgroups — C₂×C₃×C₅²×D₅₇ #30685975

Order 17100.

352 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 176 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×D₅₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₅₇	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₅²×D₁₉	—	3	1	no	maximal
5	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₅₇	C₅	1	6	yes	maximal, direct product factor
7	C₅²×D₅₇	C₂×C₃	1	2	yes	direct product factor
8	C₃×C₅²×D₁₉	—	3	2	no	—
9	C₂×C₃×C₅²×C₁₉	—	2	1	no	—
10	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₅²×D₁₉	—	3	1	no	Hall
13	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	6	yes	complemented
14	C₃×C₅×D₅₇	C₂×C₅	1	12	yes	direct product factor
15	C₃×C₅²×C₁₉	—	2	1	no	—
16	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₅×D₅₇	C₃×C₅	1	6	yes	direct product factor
19	C₂×C₃×C₅×D₁₉	—	3	6	no	—
20	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
21	C₅²×D₁₉	—	3	2	no	—
22	C₂×C₃×C₅²×D₃	—	19	1	no	maximal, Hall
23	C₃²×C₅×C₁₉	C₂²×C₅	1	6	yes	complemented
24	C₂×C₃×D₅₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅×C₁₉	—	2	6	no	—
26	C₂×C₃×C₅×C₁₉	C₅×D₃	1	6	yes	complemented
27	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
28	C₅×D₅₇	C₂×C₃×C₅	1	12	yes	direct product factor
29	C₃×C₅×D₁₉	—	3	12	no	—
30	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃²×C₅²	D₁₉	1	1	yes	characteristic, complemented
32	C₃×C₅²×D₃	—	19	2	no	—
33	C₂×C₅×D₁₉	—	3	6	no	—
34	C₂×C₃²×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented
35	C₃×D₅₇	C₂×C₅²	1	2	yes	direct product factor
36	C₂²×C₃×C₅²	—	57	1	no	—
37	C₂×C₅²×D₃	—	19	1	no	—
38	C₃×C₅×C₁₉	—	2	6	no	—
39	C₃×C₅×C₁₉	C₂×C₅×D₃	1	6	yes	complemented
40	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	complemented
41	C₂×D₅₇	C₃×C₅²	1	1	yes	characteristic, direct product factor
42	C₂×C₃×D₁₉	—	3	1	no	—
43	C₃²×C₅²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅×C₁₉	C₃×C₅×D₃	1	6	yes	complemented
45	C₅×D₁₉	—	3	12	no	—
46	C₂×C₃×C₅×D₃	—	19	6	no	—
47	C₃²×C₁₉	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅²	—	2	1	no	—
49	C₂×C₃×C₅²	—	57	2	no	—
50	C₂×C₃×C₅²	C₃×D₁₉	1	1	yes	characteristic, complemented
51	C₂×C₃×C₅²	D₅₇	1	1	yes	characteristic, direct product factor
52	C₅²×D₃	—	19	2	no	—
53	C₂×C₃×C₁₉	—	2	1	no	—
54	C₂×C₃×C₁₉	C₅²×D₃	1	1	yes	characteristic, complemented
55	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
56	D₅₇	C₂×C₃×C₅²	1	2	yes	direct product factor
57	C₃×D₁₉	—	3	2	no	—
58	C₂²×C₅²	—	57	1	no	Hall
59	C₅×C₁₉	C₂×C₃×C₅×D₃	1	6	yes	complemented
60	C₂×C₃²×C₅	C₅×D₁₉	1	6	yes	complemented
61	C₃×C₅×D₃	—	19	12	no	—
62	C₂×D₁₉	—	3	1	no	Hall
63	C₃×C₅²	—	2	1	no	—
64	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
65	C₃×C₅²	C₂×D₅₇	1	1	yes	characteristic, direct product factor
66	C₂²×C₃×C₅	—	57	6	no	—
67	C₂×C₅×D₃	—	19	6	no	—
68	C₃×C₁₉	—	2	1	no	—
69	C₃×C₁₉	C₂×C₅²×D₃	1	1	yes	characteristic, complemented
70	C₃×C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented
71	C₂×C₅²	—	57	2	no	—
72	C₂×C₅²	C₃×D₅₇	1	1	yes	characteristic, direct product factor
73	C₃²×C₅	C₂×C₅×D₁₉	1	6	yes	complemented
74	C₂×C₁₉	C₃×C₅²×D₃	1	1	yes	characteristic, complemented
75	D₁₉	—	3	2	no	—
76	C₂×C₃×D₃	—	19	1	no	Hall
77	C₂×C₃×C₅	—	2	6	no	—
78	C₂×C₃×C₅	—	57	12	no	—
79	C₂×C₃×C₅	C₃×C₅×D₁₉	1	6	yes	complemented
80	C₂×C₃×C₅	C₅×D₅₇	1	6	yes	direct product factor
81	C₅×D₃	—	19	12	no	—
82	C₅²	C₂×C₃×D₅₇	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²×C₅	—	57	6	no	—
84	C₁₉	C₂×C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₃²	C₅²×D₁₉	1	1	yes	characteristic, complemented
86	C₃×D₃	—	19	2	no	—
87	C₃×C₅	—	2	6	no	—
88	C₃×C₅	C₂×C₃×C₅×D₁₉	1	6	yes	complemented
89	C₃×C₅	C₂×C₅×D₅₇	1	6	yes	direct product factor
90	C₂²×C₃	—	57	1	no	—
91	C₂×D₃	—	19	1	no	—
92	C₂×C₅	—	57	12	no	—
93	C₂×C₅	C₃×C₅×D₅₇	1	6	yes	direct product factor
94	C₃²	C₂×C₅²×D₁₉	1	1	yes	characteristic, complemented, Sylow
95	C₂×C₃	—	2	1	no	—
96	C₂×C₃	—	57	2	no	—
97	C₂×C₃	C₃×C₅²×D₁₉	1	1	yes	characteristic, complemented
98	C₂×C₃	C₅²×D₅₇	1	1	yes	characteristic, direct product factor
99	D₃	—	19	2	no	—
100	C₅	C₂×C₃×C₅×D₅₇	1	6	yes	direct product factor
101	C₂²	—	57	1	no	Sylow
102	C₃	—	2	1	no	—
103	C₃	C₂×C₃×C₅²×D₁₉	1	1	yes	characteristic, complemented
104	C₃	C₂×C₅²×D₅₇	1	1	yes	characteristic, direct product factor
105	C₂	—	57	2	no	—
106	C₂	C₃×C₅²×D₅₇	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅²×D₅₇

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅²×D₅₇

C₃

yes

maximal, characteristic, direct product factor

C₂×C₃×C₅²×D₁₉

—

maximal

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×D₅₇

C₅

yes

maximal, direct product factor

C₅²×D₅₇

C₂×C₃

yes

direct product factor

C₃×C₅²×D₁₉

—

C₂×C₃×C₅²×C₁₉

—

C₂×C₃×C₅²×C₁₉

D₃

yes

characteristic, complemented

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₅²×D₁₉

—

Hall

C₂×C₃²×C₅×C₁₉

C₂×C₅

yes

complemented

C₃×C₅×D₅₇

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₉

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₂×C₅×D₅₇

C₃×C₅

yes

direct product factor

C₂×C₃×C₅×D₁₉

—

C₂×C₅²×C₁₉

C₃×D₃

yes

characteristic, complemented

C₅²×D₁₉

—

C₂×C₃×C₅²×D₃

—

maximal, Hall

C₃²×C₅×C₁₉

C₂²×C₅

yes

complemented

C₂×C₃×D₅₇

C₅²

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₅×D₃

yes

complemented

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

complemented

C₅×D₅₇

C₂×C₃×C₅

yes

direct product factor

C₃×C₅×D₁₉

—

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

D₁₉

yes

characteristic, complemented

C₃×C₅²×D₃

—

C₂×C₅×D₁₉

—

C₂×C₃²×C₁₉

C₂×C₅²

yes

characteristic, complemented

C₃×D₅₇

C₂×C₅²

yes

direct product factor

C₂²×C₃×C₅²

—

C₂×C₅²×D₃

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

complemented

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

complemented

C₂×D₅₇

C₃×C₅²

yes

characteristic, direct product factor

C₂×C₃×D₁₉

—

C₃²×C₅²

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

complemented

C₅×D₁₉

—

C₂×C₃×C₅×D₃

—

C₃²×C₁₉

C₂²×C₅²

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

—

C₂×C₃×C₅²

C₃×D₁₉

yes

characteristic, complemented

C₂×C₃×C₅²

D₅₇

yes

characteristic, direct product factor

C₅²×D₃

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₅²×D₃

yes

characteristic, complemented

C₂×C₃×C₁₉

C₂×C₃×C₅²

yes

characteristic, complemented

D₅₇

C₂×C₃×C₅²

yes

direct product factor

C₃×D₁₉

—

C₂²×C₅²

—

Hall

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

complemented

C₂×C₃²×C₅

C₅×D₁₉

yes

complemented

C₃×C₅×D₃

—

C₂×D₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

C₂×C₃×D₁₉

yes

characteristic, complemented

C₃×C₅²

C₂×D₅₇

yes

characteristic, direct product factor

C₂²×C₃×C₅

—

C₂×C₅×D₃

—

C₃×C₁₉

—

C₃×C₁₉

C₂×C₅²×D₃

yes

characteristic, complemented

C₃×C₁₉

C₂²×C₃×C₅²

yes

characteristic, complemented

C₂×C₅²

—

C₂×C₅²

C₃×D₅₇

yes

characteristic, direct product factor

C₃²×C₅

C₂×C₅×D₁₉

yes

complemented

C₂×C₁₉

C₃×C₅²×D₃

yes

characteristic, complemented

D₁₉

—

C₂×C₃×D₃

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₃×C₅×D₁₉

yes

complemented

C₂×C₃×C₅

C₅×D₅₇

yes

direct product factor

C₅×D₃

—

C₅²

C₂×C₃×D₅₇

yes

characteristic, direct product factor, Sylow

C₂²×C₅

—

C₁₉

C₂×C₃×C₅²×D₃

yes

characteristic, complemented, Sylow

C₂×C₃²

C₅²×D₁₉

yes

characteristic, complemented

C₃×D₃

—

C₃×C₅

—

C₃×C₅

C₂×C₃×C₅×D₁₉

yes

complemented

C₃×C₅

C₂×C₅×D₅₇

yes

direct product factor

C₂²×C₃

—

C₂×D₃

—

C₂×C₅

—

C₂×C₅

C₃×C₅×D₅₇

yes

direct product factor

C₃²

C₂×C₅²×D₁₉

yes

characteristic, complemented, Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₃×C₅²×D₁₉

yes

characteristic, complemented

C₂×C₃

C₅²×D₅₇

yes

characteristic, direct product factor

D₃

—

100

C₅

C₂×C₃×C₅×D₅₇

yes

direct product factor

101

C₂²

—

Sylow

102

C₃

—

103

C₃

C₂×C₃×C₅²×D₁₉

yes

characteristic, complemented

104

C₃

C₂×C₅²×D₅₇

yes

characteristic, direct product factor

105

C₂

—

106

C₂

C₃×C₅²×D₅₇

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₃×C₅²

subgroup

G/H

center, hypercenter

C₂×C₃×C₅²

D₅₇

commutator, cosocle, hypocenter

C₃×C₁₉

C₂²×C₃×C₅²

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅²×C₁₉

C₂

LCS

G ▷ C₃×C₁₉

UCS

C₁ ◁ C₂×C₃×C₅²

N	H ≅ G/N	type
1. C₃×C₅²×D₅₇	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₉	C₂	semidirect
3. C₂×C₅²×D₅₇	C₃	direct (N × H)
5. C₃²×C₅²×C₁₉	C₂²	semidirect
6. C₂×C₃×C₅×D₅₇	C₅	direct (N × H)
7. C₅²×D₅₇	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅²×C₁₉	D₃	semidirect
11. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
13. C₂×C₃²×C₅×C₁₉	C₂×C₅	semidirect
14. C₃×C₅×D₅₇	C₂×C₅	direct (N × H)
16. C₃×C₅²×C₁₉	C₂×D₃	semidirect
17. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
18. C₂×C₅×D₅₇	C₃×C₅	direct (N × H)
20. C₂×C₅²×C₁₉	C₃×D₃	semidirect
23. C₃²×C₅×C₁₉	C₂²×C₅	semidirect
24. C₂×C₃×D₅₇	C₅²	direct (N × H)
26. C₂×C₃×C₅×C₁₉	C₅×D₃	semidirect
27. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
28. C₅×D₅₇	C₂×C₃×C₅	direct (N × H)
30. C₅²×C₁₉	C₂×C₃×D₃	semidirect
31. C₂×C₃²×C₅²	D₁₉	semidirect
34. C₂×C₃²×C₁₉	C₂×C₅²	semidirect
35. C₃×D₅₇	C₂×C₅²	direct (N × H)
39. C₃×C₅×C₁₉	C₂×C₅×D₃	semidirect
40. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
41. C₂×D₅₇	C₃×C₅²	direct (N × H)
43. C₃²×C₅²	C₂×D₁₉	semidirect
44. C₂×C₅×C₁₉	C₃×C₅×D₃	semidirect
47. C₃²×C₁₉	C₂²×C₅²	semidirect
50. C₂×C₃×C₅²	C₃×D₁₉	semidirect
51. C₂×C₃×C₅²	D₅₇	direct (N × H)
54. C₂×C₃×C₁₉	C₅²×D₃	semidirect
55. C₂×C₃×C₁₉	C₂×C₃×C₅²	semidirect
56. D₅₇	C₂×C₃×C₅²	direct (N × H)
59. C₅×C₁₉	C₂×C₃×C₅×D₃	semidirect
60. C₂×C₃²×C₅	C₅×D₁₉	semidirect
64. C₃×C₅²	C₂×C₃×D₁₉	semidirect
65. C₃×C₅²	C₂×D₅₇	direct (N × H)
69. C₃×C₁₉	C₂×C₅²×D₃	semidirect
70. C₃×C₁₉	C₂²×C₃×C₅²	semidirect
72. C₂×C₅²	C₃×D₅₇	direct (N × H)
73. C₃²×C₅	C₂×C₅×D₁₉	semidirect
74. C₂×C₁₉	C₃×C₅²×D₃	semidirect
79. C₂×C₃×C₅	C₃×C₅×D₁₉	semidirect
80. C₂×C₃×C₅	C₅×D₅₇	direct (N × H)
82. C₅²	C₂×C₃×D₅₇	direct (N × H)
84. C₁₉	C₂×C₃×C₅²×D₃	semidirect
85. C₂×C₃²	C₅²×D₁₉	semidirect
88. C₃×C₅	C₂×C₃×C₅×D₁₉	semidirect
89. C₃×C₅	C₂×C₅×D₅₇	direct (N × H)
93. C₂×C₅	C₃×C₅×D₅₇	direct (N × H)
94. C₃²	C₂×C₅²×D₁₉	semidirect
97. C₂×C₃	C₃×C₅²×D₁₉	semidirect
98. C₂×C₃	C₅²×D₅₇	direct (N × H)
100. C₅	C₂×C₃×C₅×D₅₇	direct (N × H)
103. C₃	C₂×C₃×C₅²×D₁₉	semidirect
104. C₃	C₂×C₅²×D₅₇	direct (N × H)
106. C₂	C₃×C₅²×D₅₇	direct (N × H)

H ≅ G/N

type

1. C₃×C₅²×D₅₇

C₂

direct (N × H)

2. C₂×C₃²×C₅²×C₁₉

C₂

semidirect

3. C₂×C₅²×D₅₇

C₃

direct (N × H)

5. C₃²×C₅²×C₁₉

C₂²

semidirect

6. C₂×C₃×C₅×D₅₇

C₅

direct (N × H)

7. C₅²×D₅₇

C₂×C₃

direct (N × H)

10. C₂×C₃×C₅²×C₁₉

D₃

semidirect

11. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

13. C₂×C₃²×C₅×C₁₉

C₂×C₅

semidirect

14. C₃×C₅×D₅₇

C₂×C₅

direct (N × H)

16. C₃×C₅²×C₁₉

C₂×D₃

semidirect

17. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

18. C₂×C₅×D₅₇

C₃×C₅

direct (N × H)

20. C₂×C₅²×C₁₉

C₃×D₃

semidirect

23. C₃²×C₅×C₁₉

C₂²×C₅

semidirect

24. C₂×C₃×D₅₇

C₅²

direct (N × H)

26. C₂×C₃×C₅×C₁₉

C₅×D₃

semidirect

27. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

28. C₅×D₅₇

C₂×C₃×C₅

direct (N × H)

30. C₅²×C₁₉

C₂×C₃×D₃

semidirect

31. C₂×C₃²×C₅²

D₁₉

semidirect

34. C₂×C₃²×C₁₉

C₂×C₅²

semidirect

35. C₃×D₅₇

C₂×C₅²

direct (N × H)

39. C₃×C₅×C₁₉

C₂×C₅×D₃

semidirect

40. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

41. C₂×D₅₇

C₃×C₅²

direct (N × H)

43. C₃²×C₅²

C₂×D₁₉

semidirect

44. C₂×C₅×C₁₉

C₃×C₅×D₃

semidirect

47. C₃²×C₁₉

C₂²×C₅²

semidirect

50. C₂×C₃×C₅²

C₃×D₁₉

semidirect

51. C₂×C₃×C₅²

D₅₇

direct (N × H)

54. C₂×C₃×C₁₉

C₅²×D₃

semidirect

55. C₂×C₃×C₁₉

C₂×C₃×C₅²

semidirect

56. D₅₇

C₂×C₃×C₅²

direct (N × H)

59. C₅×C₁₉

C₂×C₃×C₅×D₃

semidirect

60. C₂×C₃²×C₅

C₅×D₁₉

semidirect

64. C₃×C₅²

C₂×C₃×D₁₉

semidirect

65. C₃×C₅²

C₂×D₅₇

direct (N × H)

69. C₃×C₁₉

C₂×C₅²×D₃

semidirect

70. C₃×C₁₉

C₂²×C₃×C₅²

semidirect

72. C₂×C₅²

C₃×D₅₇

direct (N × H)

73. C₃²×C₅

C₂×C₅×D₁₉

semidirect

74. C₂×C₁₉

C₃×C₅²×D₃

semidirect

79. C₂×C₃×C₅

C₃×C₅×D₁₉

semidirect

80. C₂×C₃×C₅

C₅×D₅₇

direct (N × H)

82. C₅²

C₂×C₃×D₅₇

direct (N × H)

84. C₁₉

C₂×C₃×C₅²×D₃

semidirect

85. C₂×C₃²

C₅²×D₁₉

semidirect

88. C₃×C₅

C₂×C₃×C₅×D₁₉

semidirect

89. C₃×C₅

C₂×C₅×D₅₇

direct (N × H)

93. C₂×C₅

C₃×C₅×D₅₇

direct (N × H)

94. C₃²

C₂×C₅²×D₁₉

semidirect

97. C₂×C₃

C₃×C₅²×D₁₉

semidirect

98. C₂×C₃

C₅²×D₅₇

direct (N × H)

100. C₅

C₂×C₃×C₅×D₅₇

direct (N × H)

103. C₃

C₂×C₃×C₅²×D₁₉

semidirect

104. C₃

C₂×C₅²×D₅₇

direct (N × H)

106. C₂

C₃×C₅²×D₅₇

direct (N × H)

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

subgroup	index
C₃×C₅²×D₅₇	2
C₂×C₃²×C₅²×C₁₉	2
C₂×C₅²×D₅₇	3
C₂×C₃×C₅²×D₁₉	3
C₂×C₃×C₅×D₅₇	5
C₂×C₃×C₅²×D₃	19

subgroup

index

C₃×C₅²×D₅₇

C₂×C₃²×C₅²×C₁₉

C₂×C₅²×D₅₇

C₂×C₃×C₅²×D₁₉

C₂×C₃×C₅×D₅₇

C₂×C₃×C₅²×D₃

Subgroups — C₂×C₃×C₅²×D₅₇ #30685975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C52×D57 #30685975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅²×D₅₇ #30685975