Group #30685840 — subgroups

Subgroups — C₂×C₅²×D₃×C₁₉⋊C₃ #30685840

Order 17100.

352 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 168 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	C₂×C₃×C₅²×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅²×D₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅²×C₁₉⋊C₃	—	3	1	no	maximal
5	C₃×C₅²×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×D₃×C₁₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
7	C₅²×D₃×C₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₅²×C₁₉⋊C₃	—	2	1	no	—
9	C₂×C₅²×C₁₉⋊C₃	—	3	2	no	—
10	C₂×C₅²×C₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂²×C₅²×C₁₉	—	3	1	no	Hall
13	C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	1	6	yes	complemented
14	C₅×D₃×C₁₉⋊C₃	C₂×C₅	1	12	yes	direct product factor
15	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₅²×C₁₉⋊C₃	—	2	1	no	—
17	C₅²×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₅×D₃×C₁₉	C₃×C₅	1	6	yes	complemented
19	C₂²×C₅×C₁₉⋊C₃	—	3	6	no	—
20	C₂×C₅²×C₁₉	—	3	2	no	—
21	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅²×D₃	—	19	1	no	maximal, Hall
23	C₃×C₅×C₁₉⋊C₃	C₂²×C₅	1	6	yes	complemented
24	C₂×D₃×C₁₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
26	C₅×D₃×C₁₉	C₂×C₃×C₅	1	12	yes	complemented
27	C₂×C₅×C₁₉⋊C₃	—	2	6	no	—
28	C₂×C₅×C₁₉⋊C₃	—	3	12	no	—
29	C₂×C₅×C₁₉⋊C₃	C₅×D₃	1	6	yes	direct product factor
30	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃²×C₅²	—	19	1	no	—
32	C₃×C₅²×D₃	—	19	2	no	—
33	C₂²×C₅×C₁₉	—	3	6	no	—
34	C₂×C₃×C₁₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented
35	D₃×C₁₉⋊C₃	C₂×C₅²	1	2	yes	direct product factor
36	C₂²×C₃×C₅²	—	57	1	no	—
37	C₂×C₅²×D₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
38	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	complemented
39	C₅×C₁₉⋊C₃	—	2	6	no	—
40	C₅×C₁₉⋊C₃	C₂×C₅×D₃	1	6	yes	direct product factor
41	C₂×D₃×C₁₉	C₃×C₅²	1	1	yes	characteristic, complemented
42	C₂²×C₁₉⋊C₃	—	3	1	no	—
43	C₃²×C₅²	—	19	1	no	Hall
44	C₂×C₅×C₁₉	—	3	12	no	—
45	C₂×C₅×C₁₉	C₃×C₅×D₃	1	6	yes	complemented
46	C₂×C₃×C₅×D₃	—	19	6	no	—
47	C₃×C₁₉⋊C₃	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅²	—	19	1	no	—
49	C₂×C₃×C₅²	—	38	1	no	—
50	C₂×C₃×C₅²	—	57	2	no	—
51	C₂×C₃×C₅²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
52	C₅²×D₃	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
53	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
54	D₃×C₁₉	C₂×C₃×C₅²	1	2	yes	complemented
55	C₂×C₁₉⋊C₃	—	2	1	no	—
56	C₂×C₁₉⋊C₃	—	3	2	no	—
57	C₂×C₁₉⋊C₃	C₅²×D₃	1	1	yes	characteristic, direct product factor
58	C₂²×C₅²	—	3	1	no	Hall
59	C₅×C₁₉	C₂×C₃×C₅×D₃	1	6	yes	complemented
60	C₂×C₃²×C₅	—	19	6	no	—
61	C₃×C₅×D₃	—	19	12	no	—
62	C₂²×C₁₉	—	3	1	no	Hall
63	C₃×C₅²	—	19	1	no	—
64	C₃×C₅²	—	38	1	no	—
65	C₃×C₅²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₅	—	57	6	no	—
67	C₂×C₅×D₃	C₅×C₁₉⋊C₃	1	6	yes	direct product factor
68	C₃×C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented
69	C₁₉⋊C₃	—	2	1	no	—
70	C₁₉⋊C₃	C₂×C₅²×D₃	1	1	yes	characteristic, direct product factor
71	C₂×C₅²	—	3	2	no	—
72	C₂×C₅²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
73	C₃²×C₅	—	19	6	no	—
74	C₂×C₁₉	—	3	2	no	—
75	C₂×C₁₉	C₃×C₅²×D₃	1	1	yes	characteristic, complemented
76	C₂×C₃×D₃	—	19	1	no	Hall
77	C₂×C₃×C₅	—	19	6	no	—
78	C₂×C₃×C₅	—	38	6	no	—
79	C₂×C₃×C₅	—	57	12	no	—
80	C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	1	6	yes	complemented
81	C₅×D₃	C₂×C₅×C₁₉⋊C₃	1	12	yes	direct product factor
82	C₅²	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²×C₅	—	3	6	no	—
84	C₁₉	C₂×C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₃²	—	19	1	no	—
86	C₃×D₃	—	19	2	no	—
87	C₃×C₅	—	19	6	no	—
88	C₃×C₅	—	38	6	no	—
89	C₃×C₅	C₂²×C₅×C₁₉⋊C₃	1	6	yes	complemented
90	C₂²×C₃	—	57	1	no	—
91	C₂×D₃	C₅²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
92	C₂×C₅	—	3	12	no	—
93	C₂×C₅	C₅×D₃×C₁₉⋊C₃	1	6	yes	direct product factor
94	C₃²	—	19	1	no	Sylow
95	C₂×C₃	—	19	1	no	—
96	C₂×C₃	—	38	1	no	—
97	C₂×C₃	—	57	2	no	—
98	C₂×C₃	C₂×C₅²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
99	D₃	C₂×C₅²×C₁₉⋊C₃	1	2	yes	direct product factor
100	C₅	C₂×C₅×D₃×C₁₉⋊C₃	1	6	yes	direct product factor
101	C₂²	—	3	1	no	Sylow
102	C₃	—	19	1	no	—
103	C₃	—	38	1	no	—
104	C₃	C₂²×C₅²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
105	C₂	—	3	2	no	—
106	C₂	C₅²×D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃×C₅²×C₁₉⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅²×D₃×C₁₉⋊C₃

C₂

yes

maximal, direct product factor

C₂×C₅²×D₃×C₁₉

C₃

yes

maximal, characteristic, complemented

C₂²×C₅²×C₁₉⋊C₃

—

maximal

C₃×C₅²×C₁₉⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₁₉⋊C₃

C₅

yes

maximal, direct product factor

C₅²×D₃×C₁₉

C₂×C₃

yes

complemented

C₂×C₅²×C₁₉⋊C₃

—

C₂×C₅²×C₁₉⋊C₃

—

C₂×C₅²×C₁₉⋊C₃

D₃

yes

characteristic, direct product factor

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂²×C₅²×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

yes

complemented

C₅×D₃×C₁₉⋊C₃

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₅²×C₁₉⋊C₃

—

C₅²×C₁₉⋊C₃

C₂×D₃

yes

characteristic, direct product factor

C₂×C₅×D₃×C₁₉

C₃×C₅

yes

complemented

C₂²×C₅×C₁₉⋊C₃

—

C₂×C₅²×C₁₉

—

C₂×C₅²×C₁₉

C₃×D₃

yes

characteristic, complemented

C₂×C₃×C₅²×D₃

—

maximal, Hall

C₃×C₅×C₁₉⋊C₃

C₂²×C₅

yes

complemented

C₂×D₃×C₁₉⋊C₃

C₅²

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

complemented

C₅×D₃×C₁₉

C₂×C₃×C₅

yes

complemented

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

C₅×D₃

yes

direct product factor

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

—

C₃×C₅²×D₃

—

C₂²×C₅×C₁₉

—

C₂×C₃×C₁₉⋊C₃

C₂×C₅²

yes

characteristic, complemented

D₃×C₁₉⋊C₃

C₂×C₅²

yes

direct product factor

C₂²×C₃×C₅²

—

C₂×C₅²×D₃

C₁₉⋊C₃

yes

characteristic, direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

complemented

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

C₂×C₅×D₃

yes

direct product factor

C₂×D₃×C₁₉

C₃×C₅²

yes

characteristic, complemented

C₂²×C₁₉⋊C₃

—

C₃²×C₅²

—

Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

complemented

C₂×C₃×C₅×D₃

—

C₃×C₁₉⋊C₃

C₂²×C₅²

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

—

C₂×C₃×C₅²

—

C₂×C₃×C₅²

C₂×C₁₉⋊C₃

yes

characteristic, complemented

C₅²×D₃

C₂×C₁₉⋊C₃

yes

direct product factor

C₂×C₃×C₁₉

C₂×C₃×C₅²

yes

characteristic, complemented

D₃×C₁₉

C₂×C₃×C₅²

yes

complemented

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

C₅²×D₃

yes

characteristic, direct product factor

C₂²×C₅²

—

Hall

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

complemented

C₂×C₃²×C₅

—

C₃×C₅×D₃

—

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

—

C₃×C₅²

C₂²×C₁₉⋊C₃

yes

characteristic, complemented

C₂²×C₃×C₅

—

C₂×C₅×D₃

C₅×C₁₉⋊C₃

yes

direct product factor

C₃×C₁₉

C₂²×C₃×C₅²

yes

characteristic, complemented

C₁₉⋊C₃

—

C₁₉⋊C₃

C₂×C₅²×D₃

yes

characteristic, direct product factor

C₂×C₅²

—

C₂×C₅²

D₃×C₁₉⋊C₃

yes

characteristic, direct product factor

C₃²×C₅

—

C₂×C₁₉

—

C₂×C₁₉

C₃×C₅²×D₃

yes

characteristic, complemented

C₂×C₃×D₃

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

yes

complemented

C₅×D₃

C₂×C₅×C₁₉⋊C₃

yes

direct product factor

C₅²

C₂×D₃×C₁₉⋊C₃

yes

characteristic, direct product factor, Sylow

C₂²×C₅

—

C₁₉

C₂×C₃×C₅²×D₃

yes

characteristic, complemented, Sylow

C₂×C₃²

—

C₃×D₃

—

C₃×C₅

—

C₃×C₅

—

C₃×C₅

C₂²×C₅×C₁₉⋊C₃

yes

complemented

C₂²×C₃

—

C₂×D₃

C₅²×C₁₉⋊C₃

yes

characteristic, direct product factor

C₂×C₅

—

C₂×C₅

C₅×D₃×C₁₉⋊C₃

yes

direct product factor

C₃²

—

Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₂×C₅²×C₁₉⋊C₃

yes

characteristic, complemented

D₃

C₂×C₅²×C₁₉⋊C₃

yes

direct product factor

100

C₅

C₂×C₅×D₃×C₁₉⋊C₃

yes

direct product factor

101

C₂²

—

Sylow

102

C₃

—

103

C₃

—

104

C₃

C₂²×C₅²×C₁₉⋊C₃

yes

characteristic, complemented

105

C₂

—

106

C₂

C₅²×D₃×C₁₉⋊C₃

yes

characteristic, direct product factor

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

subgroup

G/H

center, hypercenter

C₂×C₅²

D₃×C₁₉⋊C₃

commutator, cosocle, hypocenter

C₃×C₁₉

C₂²×C₃×C₅²

Frattini

C₁

Fitting, socle

C₂×C₃×C₅²×C₁₉

C₂×C₃

LCS

G ▷ C₃×C₁₉

UCS

C₁ ◁ C₂×C₅²

N	H ≅ G/N	type
1. C₂×C₃×C₅²×C₁₉⋊C₃	C₂	semidirect
2. C₅²×D₃×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₅²×D₃×C₁₉	C₃	semidirect
5. C₃×C₅²×C₁₉⋊C₃	C₂²	semidirect
6. C₂×C₅×D₃×C₁₉⋊C₃	C₅	direct (N × H)
7. C₅²×D₃×C₁₉	C₂×C₃	semidirect
10. C₂×C₅²×C₁₉⋊C₃	D₃	direct (N × H)
11. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
13. C₂×C₃×C₅×C₁₉⋊C₃	C₂×C₅	semidirect
14. C₅×D₃×C₁₉⋊C₃	C₂×C₅	direct (N × H)
15. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
17. C₅²×C₁₉⋊C₃	C₂×D₃	direct (N × H)
18. C₂×C₅×D₃×C₁₉	C₃×C₅	semidirect
21. C₂×C₅²×C₁₉	C₃×D₃	semidirect
23. C₃×C₅×C₁₉⋊C₃	C₂²×C₅	semidirect
24. C₂×D₃×C₁₉⋊C₃	C₅²	direct (N × H)
25. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
26. C₅×D₃×C₁₉	C₂×C₃×C₅	semidirect
29. C₂×C₅×C₁₉⋊C₃	C₅×D₃	direct (N × H)
30. C₅²×C₁₉	C₂×C₃×D₃	semidirect
34. C₂×C₃×C₁₉⋊C₃	C₂×C₅²	semidirect
35. D₃×C₁₉⋊C₃	C₂×C₅²	direct (N × H)
37. C₂×C₅²×D₃	C₁₉⋊C₃	direct (N × H)
38. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
40. C₅×C₁₉⋊C₃	C₂×C₅×D₃	direct (N × H)
41. C₂×D₃×C₁₉	C₃×C₅²	semidirect
45. C₂×C₅×C₁₉	C₃×C₅×D₃	semidirect
47. C₃×C₁₉⋊C₃	C₂²×C₅²	semidirect
51. C₂×C₃×C₅²	C₂×C₁₉⋊C₃	semidirect
52. C₅²×D₃	C₂×C₁₉⋊C₃	direct (N × H)
53. C₂×C₃×C₁₉	C₂×C₃×C₅²	semidirect
54. D₃×C₁₉	C₂×C₃×C₅²	semidirect
57. C₂×C₁₉⋊C₃	C₅²×D₃	direct (N × H)
59. C₅×C₁₉	C₂×C₃×C₅×D₃	semidirect
65. C₃×C₅²	C₂²×C₁₉⋊C₃	semidirect
67. C₂×C₅×D₃	C₅×C₁₉⋊C₃	direct (N × H)
68. C₃×C₁₉	C₂²×C₃×C₅²	semidirect
70. C₁₉⋊C₃	C₂×C₅²×D₃	direct (N × H)
72. C₂×C₅²	D₃×C₁₉⋊C₃	direct (N × H)
75. C₂×C₁₉	C₃×C₅²×D₃	semidirect
80. C₂×C₃×C₅	C₂×C₅×C₁₉⋊C₃	semidirect
81. C₅×D₃	C₂×C₅×C₁₉⋊C₃	direct (N × H)
82. C₅²	C₂×D₃×C₁₉⋊C₃	direct (N × H)
84. C₁₉	C₂×C₃×C₅²×D₃	semidirect
89. C₃×C₅	C₂²×C₅×C₁₉⋊C₃	semidirect
91. C₂×D₃	C₅²×C₁₉⋊C₃	direct (N × H)
93. C₂×C₅	C₅×D₃×C₁₉⋊C₃	direct (N × H)
98. C₂×C₃	C₂×C₅²×C₁₉⋊C₃	semidirect
99. D₃	C₂×C₅²×C₁₉⋊C₃	direct (N × H)
100. C₅	C₂×C₅×D₃×C₁₉⋊C₃	direct (N × H)
104. C₃	C₂²×C₅²×C₁₉⋊C₃	semidirect
106. C₂	C₅²×D₃×C₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₂×C₃×C₅²×C₁₉⋊C₃

C₂

semidirect

2. C₅²×D₃×C₁₉⋊C₃

C₂

direct (N × H)

3. C₂×C₅²×D₃×C₁₉

C₃

semidirect

5. C₃×C₅²×C₁₉⋊C₃

C₂²

semidirect

6. C₂×C₅×D₃×C₁₉⋊C₃

C₅

direct (N × H)

7. C₅²×D₃×C₁₉

C₂×C₃

semidirect

10. C₂×C₅²×C₁₉⋊C₃

D₃

direct (N × H)

11. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

13. C₂×C₃×C₅×C₁₉⋊C₃

C₂×C₅

semidirect

14. C₅×D₃×C₁₉⋊C₃

C₂×C₅

direct (N × H)

15. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

17. C₅²×C₁₉⋊C₃

C₂×D₃

direct (N × H)

18. C₂×C₅×D₃×C₁₉

C₃×C₅

semidirect

21. C₂×C₅²×C₁₉

C₃×D₃

semidirect

23. C₃×C₅×C₁₉⋊C₃

C₂²×C₅

semidirect

24. C₂×D₃×C₁₉⋊C₃

C₅²

direct (N × H)

25. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

26. C₅×D₃×C₁₉

C₂×C₃×C₅

semidirect

29. C₂×C₅×C₁₉⋊C₃

C₅×D₃

direct (N × H)

30. C₅²×C₁₉

C₂×C₃×D₃

semidirect

34. C₂×C₃×C₁₉⋊C₃

C₂×C₅²

semidirect

35. D₃×C₁₉⋊C₃

C₂×C₅²

direct (N × H)

37. C₂×C₅²×D₃

C₁₉⋊C₃

direct (N × H)

38. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

40. C₅×C₁₉⋊C₃

C₂×C₅×D₃

direct (N × H)

41. C₂×D₃×C₁₉

C₃×C₅²

semidirect

45. C₂×C₅×C₁₉

C₃×C₅×D₃

semidirect

47. C₃×C₁₉⋊C₃

C₂²×C₅²

semidirect

51. C₂×C₃×C₅²

C₂×C₁₉⋊C₃

semidirect

52. C₅²×D₃

C₂×C₁₉⋊C₃

direct (N × H)

53. C₂×C₃×C₁₉

C₂×C₃×C₅²

semidirect

54. D₃×C₁₉

C₂×C₃×C₅²

semidirect

57. C₂×C₁₉⋊C₃

C₅²×D₃

direct (N × H)

59. C₅×C₁₉

C₂×C₃×C₅×D₃

semidirect

65. C₃×C₅²

C₂²×C₁₉⋊C₃

semidirect

67. C₂×C₅×D₃

C₅×C₁₉⋊C₃

direct (N × H)

68. C₃×C₁₉

C₂²×C₃×C₅²

semidirect

70. C₁₉⋊C₃

C₂×C₅²×D₃

direct (N × H)

72. C₂×C₅²

D₃×C₁₉⋊C₃

direct (N × H)

75. C₂×C₁₉

C₃×C₅²×D₃

semidirect

80. C₂×C₃×C₅

C₂×C₅×C₁₉⋊C₃

semidirect

81. C₅×D₃

C₂×C₅×C₁₉⋊C₃

direct (N × H)

82. C₅²

C₂×D₃×C₁₉⋊C₃

direct (N × H)

84. C₁₉

C₂×C₃×C₅²×D₃

semidirect

89. C₃×C₅

C₂²×C₅×C₁₉⋊C₃

semidirect

91. C₂×D₃

C₅²×C₁₉⋊C₃

direct (N × H)

93. C₂×C₅

C₅×D₃×C₁₉⋊C₃

direct (N × H)

98. C₂×C₃

C₂×C₅²×C₁₉⋊C₃

semidirect

99. D₃

C₂×C₅²×C₁₉⋊C₃

direct (N × H)

100. C₅

C₂×C₅×D₃×C₁₉⋊C₃

direct (N × H)

104. C₃

C₂²×C₅²×C₁₉⋊C₃

semidirect

106. C₂

C₅²×D₃×C₁₉⋊C₃

direct (N × H)

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

subgroup	index
C₂×C₃×C₅²×C₁₉⋊C₃	2
C₅²×D₃×C₁₉⋊C₃	2
C₂×C₅²×D₃×C₁₉	3
C₂²×C₅²×C₁₉⋊C₃	3
C₂×C₅×D₃×C₁₉⋊C₃	5
C₂×C₃×C₅²×D₃	19

subgroup

index

C₂×C₃×C₅²×C₁₉⋊C₃

C₅²×D₃×C₁₉⋊C₃

C₂×C₅²×D₃×C₁₉

C₂²×C₅²×C₁₉⋊C₃

C₂×C₅×D₃×C₁₉⋊C₃

C₂×C₃×C₅²×D₃

Subgroups — C₂×C₅²×D₃×C₁₉⋊C₃ #30685840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C52×D3×C19⋊C3 #30685840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×D₃×C₁₉⋊C₃ #30685840