Group #30685976 — subgroups

Subgroups — C₂×C₃×C₅²×D₃×C₁₉ #30685976

Order 17100.

352 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 224 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×D₃×C₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×D₃×C₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂²×C₃×C₅²×C₁₉	—	3	1	no	maximal
5	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅×D₃×C₁₉	C₅	1	6	yes	maximal, direct product factor
7	C₅²×D₃×C₁₉	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅²×C₁₉	—	2	1	no	—
9	C₂×C₃×C₅²×C₁₉	—	3	2	no	—
10	C₂×C₃×C₅²×C₁₉	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×C₃²×C₅×C₁₉	C₂×C₅	1	6	yes	complemented
14	C₃×C₅×D₃×C₁₉	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, direct product factor
17	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅×C₁₉	—	3	6	no	—
19	C₂×C₅×D₃×C₁₉	C₃×C₅	1	6	yes	direct product factor
20	C₂×C₅²×C₁₉	—	3	2	no	—
21	C₂×C₅²×C₁₉	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₂×C₃×C₅²×D₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₃²×C₅×C₁₉	C₂²×C₅	1	6	yes	complemented
24	C₂×C₃×D₃×C₁₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₅×C₁₉	—	2	6	no	—
26	C₂×C₃×C₅×C₁₉	—	3	12	no	—
27	C₂×C₃×C₅×C₁₉	C₅×D₃	1	6	yes	direct product factor
28	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
29	C₅×D₃×C₁₉	C₂×C₃×C₅	1	12	yes	direct product factor
30	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₅²	C₂×C₁₉	1	1	yes	characteristic, complemented
32	C₃×C₅²×D₃	C₂×C₁₉	1	2	yes	direct product factor
33	C₂²×C₅×C₁₉	—	3	6	no	—
34	C₂×C₃²×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented
35	C₃×D₃×C₁₉	C₂×C₅²	1	2	yes	direct product factor
36	C₂²×C₃×C₅²	—	3	1	no	—
37	C₂×C₅²×D₃	C₃×C₁₉	1	1	yes	characteristic, direct product factor
38	C₃×C₅×C₁₉	—	2	6	no	—
39	C₃×C₅×C₁₉	C₂×C₅×D₃	1	6	yes	direct product factor
40	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	6	yes	complemented
41	C₂²×C₃×C₁₉	—	3	1	no	—
42	C₂×D₃×C₁₉	C₃×C₅²	1	1	yes	characteristic, direct product factor
43	C₃²×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅×C₁₉	—	3	12	no	—
45	C₂×C₅×C₁₉	C₃×C₅×D₃	1	6	yes	direct product factor
46	C₂×C₃×C₅×D₃	C₅×C₁₉	1	6	yes	direct product factor
47	C₃²×C₁₉	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₅²	—	2	1	no	—
49	C₂×C₃×C₅²	—	3	2	no	—
50	C₂×C₃×C₅²	D₃×C₁₉	1	1	yes	characteristic, direct product factor
51	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	1	yes	characteristic, complemented
52	C₅²×D₃	C₂×C₃×C₁₉	1	2	yes	direct product factor
53	C₂×C₃×C₁₉	—	2	1	no	—
54	C₂×C₃×C₁₉	—	3	2	no	—
55	C₂×C₃×C₁₉	C₅²×D₃	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
57	D₃×C₁₉	C₂×C₃×C₅²	1	2	yes	direct product factor
58	C₂²×C₅²	—	3	1	no	Hall
59	C₅×C₁₉	C₂×C₃×C₅×D₃	1	6	yes	direct product factor
60	C₂×C₃²×C₅	C₂×C₅×C₁₉	1	6	yes	complemented
61	C₃×C₅×D₃	C₂×C₅×C₁₉	1	12	yes	direct product factor
62	C₂²×C₁₉	—	3	1	no	Hall
63	C₃×C₅²	—	2	1	no	—
64	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic, direct product factor
65	C₃×C₅²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented
66	C₂²×C₃×C₅	—	3	6	no	—
67	C₂×C₅×D₃	C₃×C₅×C₁₉	1	6	yes	direct product factor
68	C₃×C₁₉	—	2	1	no	—
69	C₃×C₁₉	C₂×C₅²×D₃	1	1	yes	characteristic, direct product factor
70	C₃×C₁₉	C₂²×C₃×C₅²	1	1	yes	characteristic, complemented
71	C₂×C₅²	—	3	2	no	—
72	C₂×C₅²	C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor
73	C₃²×C₅	C₂²×C₅×C₁₉	1	6	yes	complemented
74	C₂×C₁₉	—	3	2	no	—
75	C₂×C₁₉	C₃×C₅²×D₃	1	1	yes	characteristic, direct product factor
76	C₂×C₃×D₃	C₅²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
77	C₂×C₃×C₅	—	2	6	no	—
78	C₂×C₃×C₅	—	3	12	no	—
79	C₂×C₃×C₅	C₅×D₃×C₁₉	1	6	yes	direct product factor
80	C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	1	6	yes	complemented
81	C₅×D₃	C₂×C₃×C₅×C₁₉	1	12	yes	direct product factor
82	C₅²	C₂×C₃×D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²×C₅	—	3	6	no	—
84	C₁₉	C₂×C₃×C₅²×D₃	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₃²	C₂×C₅²×C₁₉	1	1	yes	characteristic, complemented
86	C₃×D₃	C₂×C₅²×C₁₉	1	2	yes	direct product factor
87	C₃×C₅	—	2	6	no	—
88	C₃×C₅	C₂×C₅×D₃×C₁₉	1	6	yes	direct product factor
89	C₃×C₅	C₂²×C₃×C₅×C₁₉	1	6	yes	complemented
90	C₂²×C₃	—	3	1	no	—
91	C₂×D₃	C₃×C₅²×C₁₉	1	1	yes	characteristic, direct product factor
92	C₂×C₅	—	3	12	no	—
93	C₂×C₅	C₃×C₅×D₃×C₁₉	1	6	yes	direct product factor
94	C₃²	C₂²×C₅²×C₁₉	1	1	yes	characteristic, complemented, Sylow
95	C₂×C₃	—	2	1	no	—
96	C₂×C₃	—	3	2	no	—
97	C₂×C₃	C₂×C₃×C₅²×C₁₉	1	1	yes	characteristic, complemented
98	C₂×C₃	C₅²×D₃×C₁₉	1	1	yes	characteristic, direct product factor
99	D₃	C₂×C₃×C₅²×C₁₉	1	2	yes	direct product factor
100	C₅	C₂×C₃×C₅×D₃×C₁₉	1	6	yes	direct product factor
101	C₂²	—	3	1	no	Sylow
102	C₃	—	2	1	no	—
103	C₃	C₂²×C₃×C₅²×C₁₉	1	1	yes	characteristic, complemented
104	C₃	C₂×C₅²×D₃×C₁₉	1	1	yes	characteristic, direct product factor
105	C₂	—	3	2	no	—
106	C₂	C₃×C₅²×D₃×C₁₉	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅²×D₃×C₁₉

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅²×D₃×C₁₉

C₃

yes

maximal, characteristic, direct product factor

C₂²×C₃×C₅²×C₁₉

—

maximal

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×D₃×C₁₉

C₅

yes

maximal, direct product factor

C₅²×D₃×C₁₉

C₂×C₃

yes

direct product factor

C₂×C₃×C₅²×C₁₉

—

C₂×C₃×C₅²×C₁₉

—

C₂×C₃×C₅²×C₁₉

D₃

yes

characteristic, direct product factor

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

characteristic, complemented

C₂²×C₅²×C₁₉

—

Hall

C₂×C₃²×C₅×C₁₉

C₂×C₅

yes

complemented

C₃×C₅×D₃×C₁₉

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₉

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic, direct product factor

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₂²×C₃×C₅×C₁₉

—

C₂×C₅×D₃×C₁₉

C₃×C₅

yes

direct product factor

C₂×C₅²×C₁₉

—

C₂×C₅²×C₁₉

C₃×D₃

yes

characteristic, direct product factor

C₂×C₃×C₅²×D₃

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₅×C₁₉

C₂²×C₅

yes

complemented

C₂×C₃×D₃×C₁₉

C₅²

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₅×D₃

yes

direct product factor

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

complemented

C₅×D₃×C₁₉

C₂×C₃×C₅

yes

direct product factor

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₅²

C₂×C₁₉

yes

characteristic, complemented

C₃×C₅²×D₃

C₂×C₁₉

yes

direct product factor

C₂²×C₅×C₁₉

—

C₂×C₃²×C₁₉

C₂×C₅²

yes

characteristic, complemented

C₃×D₃×C₁₉

C₂×C₅²

yes

direct product factor

C₂²×C₃×C₅²

—

C₂×C₅²×D₃

C₃×C₁₉

yes

characteristic, direct product factor

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

complemented

C₂²×C₃×C₁₉

—

C₂×D₃×C₁₉

C₃×C₅²

yes

characteristic, direct product factor

C₃²×C₅²

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃×C₅×D₃

yes

direct product factor

C₂×C₃×C₅×D₃

C₅×C₁₉

yes

direct product factor

C₃²×C₁₉

C₂²×C₅²

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₂×C₃×C₅²

—

C₂×C₃×C₅²

D₃×C₁₉

yes

characteristic, direct product factor

C₂×C₃×C₅²

C₂×C₃×C₁₉

yes

characteristic, complemented

C₅²×D₃

C₂×C₃×C₁₉

yes

direct product factor

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₅²×D₃

yes

characteristic, direct product factor

C₂×C₃×C₁₉

C₂×C₃×C₅²

yes

characteristic, complemented

D₃×C₁₉

C₂×C₃×C₅²

yes

direct product factor

C₂²×C₅²

—

Hall

C₅×C₁₉

C₂×C₃×C₅×D₃

yes

direct product factor

C₂×C₃²×C₅

C₂×C₅×C₁₉

yes

complemented

C₃×C₅×D₃

C₂×C₅×C₁₉

yes

direct product factor

C₂²×C₁₉

—

Hall

C₃×C₅²

—

C₃×C₅²

C₂×D₃×C₁₉

yes

characteristic, direct product factor

C₃×C₅²

C₂²×C₃×C₁₉

yes

characteristic, complemented

C₂²×C₃×C₅

—

C₂×C₅×D₃

C₃×C₅×C₁₉

yes

direct product factor

C₃×C₁₉

—

C₃×C₁₉

C₂×C₅²×D₃

yes

characteristic, direct product factor

C₃×C₁₉

C₂²×C₃×C₅²

yes

characteristic, complemented

C₂×C₅²

—

C₂×C₅²

C₃×D₃×C₁₉

yes

characteristic, direct product factor

C₃²×C₅

C₂²×C₅×C₁₉

yes

complemented

C₂×C₁₉

—

C₂×C₁₉

C₃×C₅²×D₃

yes

characteristic, direct product factor

C₂×C₃×D₃

C₅²×C₁₉

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₅×D₃×C₁₉

yes

direct product factor

C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

yes

complemented

C₅×D₃

C₂×C₃×C₅×C₁₉

yes

direct product factor

C₅²

C₂×C₃×D₃×C₁₉

yes

characteristic, direct product factor, Sylow

C₂²×C₅

—

C₁₉

C₂×C₃×C₅²×D₃

yes

characteristic, direct product factor, Sylow

C₂×C₃²

C₂×C₅²×C₁₉

yes

characteristic, complemented

C₃×D₃

C₂×C₅²×C₁₉

yes

direct product factor

C₃×C₅

—

C₃×C₅

C₂×C₅×D₃×C₁₉

yes

direct product factor

C₃×C₅

C₂²×C₃×C₅×C₁₉

yes

complemented

C₂²×C₃

—

C₂×D₃

C₃×C₅²×C₁₉

yes

characteristic, direct product factor

C₂×C₅

—

C₂×C₅

C₃×C₅×D₃×C₁₉

yes

direct product factor

C₃²

C₂²×C₅²×C₁₉

yes

characteristic, complemented, Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

C₂×C₃×C₅²×C₁₉

yes

characteristic, complemented

C₂×C₃

C₅²×D₃×C₁₉

yes

characteristic, direct product factor

D₃

C₂×C₃×C₅²×C₁₉

yes

direct product factor

100

C₅

C₂×C₃×C₅×D₃×C₁₉

yes

direct product factor

101

C₂²

—

Sylow

102

C₃

—

103

C₃

C₂²×C₃×C₅²×C₁₉

yes

characteristic, complemented

104

C₃

C₂×C₅²×D₃×C₁₉

yes

characteristic, direct product factor

105

C₂

—

106

C₂

C₃×C₅²×D₃×C₁₉

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅²×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₃×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₅²×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₃×C₅²×C₁₉

D₃

commutator, cosocle, hypocenter

C₃

C₂²×C₃×C₅²×C₁₉

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅²×C₁₉

C₂

LCS

G ▷ C₃

UCS

C₁ ◁ C₂×C₃×C₅²×C₁₉

N	H ≅ G/N	type
1. C₃×C₅²×D₃×C₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₉	C₂	semidirect
3. C₂×C₅²×D₃×C₁₉	C₃	direct (N × H)
5. C₃²×C₅²×C₁₉	C₂²	semidirect
6. C₂×C₃×C₅×D₃×C₁₉	C₅	direct (N × H)
7. C₅²×D₃×C₁₉	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅²×C₁₉	D₃	direct (N × H)
11. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
13. C₂×C₃²×C₅×C₁₉	C₂×C₅	semidirect
14. C₃×C₅×D₃×C₁₉	C₂×C₅	direct (N × H)
16. C₃×C₅²×C₁₉	C₂×D₃	direct (N × H)
17. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
19. C₂×C₅×D₃×C₁₉	C₃×C₅	direct (N × H)
21. C₂×C₅²×C₁₉	C₃×D₃	direct (N × H)
22. C₂×C₃×C₅²×D₃	C₁₉	direct (N × H)
23. C₃²×C₅×C₁₉	C₂²×C₅	semidirect
24. C₂×C₃×D₃×C₁₉	C₅²	direct (N × H)
27. C₂×C₃×C₅×C₁₉	C₅×D₃	direct (N × H)
28. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
29. C₅×D₃×C₁₉	C₂×C₃×C₅	direct (N × H)
30. C₅²×C₁₉	C₂×C₃×D₃	direct (N × H)
31. C₂×C₃²×C₅²	C₂×C₁₉	semidirect
32. C₃×C₅²×D₃	C₂×C₁₉	direct (N × H)
34. C₂×C₃²×C₁₉	C₂×C₅²	semidirect
35. C₃×D₃×C₁₉	C₂×C₅²	direct (N × H)
37. C₂×C₅²×D₃	C₃×C₁₉	direct (N × H)
39. C₃×C₅×C₁₉	C₂×C₅×D₃	direct (N × H)
40. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
42. C₂×D₃×C₁₉	C₃×C₅²	direct (N × H)
43. C₃²×C₅²	C₂²×C₁₉	semidirect
45. C₂×C₅×C₁₉	C₃×C₅×D₃	direct (N × H)
46. C₂×C₃×C₅×D₃	C₅×C₁₉	direct (N × H)
47. C₃²×C₁₉	C₂²×C₅²	semidirect
50. C₂×C₃×C₅²	D₃×C₁₉	direct (N × H)
51. C₂×C₃×C₅²	C₂×C₃×C₁₉	semidirect
52. C₅²×D₃	C₂×C₃×C₁₉	direct (N × H)
55. C₂×C₃×C₁₉	C₅²×D₃	direct (N × H)
56. C₂×C₃×C₁₉	C₂×C₃×C₅²	semidirect
57. D₃×C₁₉	C₂×C₃×C₅²	direct (N × H)
59. C₅×C₁₉	C₂×C₃×C₅×D₃	direct (N × H)
60. C₂×C₃²×C₅	C₂×C₅×C₁₉	semidirect
61. C₃×C₅×D₃	C₂×C₅×C₁₉	direct (N × H)
64. C₃×C₅²	C₂×D₃×C₁₉	direct (N × H)
65. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
67. C₂×C₅×D₃	C₃×C₅×C₁₉	direct (N × H)
69. C₃×C₁₉	C₂×C₅²×D₃	direct (N × H)
70. C₃×C₁₉	C₂²×C₃×C₅²	semidirect
72. C₂×C₅²	C₃×D₃×C₁₉	direct (N × H)
73. C₃²×C₅	C₂²×C₅×C₁₉	semidirect
75. C₂×C₁₉	C₃×C₅²×D₃	direct (N × H)
76. C₂×C₃×D₃	C₅²×C₁₉	direct (N × H)
79. C₂×C₃×C₅	C₅×D₃×C₁₉	direct (N × H)
80. C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	semidirect
81. C₅×D₃	C₂×C₃×C₅×C₁₉	direct (N × H)
82. C₅²	C₂×C₃×D₃×C₁₉	direct (N × H)
84. C₁₉	C₂×C₃×C₅²×D₃	direct (N × H)
85. C₂×C₃²	C₂×C₅²×C₁₉	semidirect
86. C₃×D₃	C₂×C₅²×C₁₉	direct (N × H)
88. C₃×C₅	C₂×C₅×D₃×C₁₉	direct (N × H)
89. C₃×C₅	C₂²×C₃×C₅×C₁₉	semidirect
91. C₂×D₃	C₃×C₅²×C₁₉	direct (N × H)
93. C₂×C₅	C₃×C₅×D₃×C₁₉	direct (N × H)
94. C₃²	C₂²×C₅²×C₁₉	semidirect
97. C₂×C₃	C₂×C₃×C₅²×C₁₉	semidirect
98. C₂×C₃	C₅²×D₃×C₁₉	direct (N × H)
99. D₃	C₂×C₃×C₅²×C₁₉	direct (N × H)
100. C₅	C₂×C₃×C₅×D₃×C₁₉	direct (N × H)
103. C₃	C₂²×C₃×C₅²×C₁₉	semidirect
104. C₃	C₂×C₅²×D₃×C₁₉	direct (N × H)
106. C₂	C₃×C₅²×D₃×C₁₉	direct (N × H)

H ≅ G/N

type

1. C₃×C₅²×D₃×C₁₉

C₂

direct (N × H)

2. C₂×C₃²×C₅²×C₁₉

C₂

semidirect

3. C₂×C₅²×D₃×C₁₉

C₃

direct (N × H)

5. C₃²×C₅²×C₁₉

C₂²

semidirect

6. C₂×C₃×C₅×D₃×C₁₉

C₅

direct (N × H)

7. C₅²×D₃×C₁₉

C₂×C₃

direct (N × H)

10. C₂×C₃×C₅²×C₁₉

D₃

direct (N × H)

11. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

13. C₂×C₃²×C₅×C₁₉

C₂×C₅

semidirect

14. C₃×C₅×D₃×C₁₉

C₂×C₅

direct (N × H)

16. C₃×C₅²×C₁₉

C₂×D₃

direct (N × H)

17. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

19. C₂×C₅×D₃×C₁₉

C₃×C₅

direct (N × H)

21. C₂×C₅²×C₁₉

C₃×D₃

direct (N × H)

22. C₂×C₃×C₅²×D₃

C₁₉

direct (N × H)

23. C₃²×C₅×C₁₉

C₂²×C₅

semidirect

24. C₂×C₃×D₃×C₁₉

C₅²

direct (N × H)

27. C₂×C₃×C₅×C₁₉

C₅×D₃

direct (N × H)

28. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

29. C₅×D₃×C₁₉

C₂×C₃×C₅

direct (N × H)

30. C₅²×C₁₉

C₂×C₃×D₃

direct (N × H)

31. C₂×C₃²×C₅²

C₂×C₁₉

semidirect

32. C₃×C₅²×D₃

C₂×C₁₉

direct (N × H)

34. C₂×C₃²×C₁₉

C₂×C₅²

semidirect

35. C₃×D₃×C₁₉

C₂×C₅²

direct (N × H)

37. C₂×C₅²×D₃

C₃×C₁₉

direct (N × H)

39. C₃×C₅×C₁₉

C₂×C₅×D₃

direct (N × H)

40. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

42. C₂×D₃×C₁₉

C₃×C₅²

direct (N × H)

43. C₃²×C₅²

C₂²×C₁₉

semidirect

45. C₂×C₅×C₁₉

C₃×C₅×D₃

direct (N × H)

46. C₂×C₃×C₅×D₃

C₅×C₁₉

direct (N × H)

47. C₃²×C₁₉

C₂²×C₅²

semidirect

50. C₂×C₃×C₅²

D₃×C₁₉

direct (N × H)

51. C₂×C₃×C₅²

C₂×C₃×C₁₉

semidirect

52. C₅²×D₃

C₂×C₃×C₁₉

direct (N × H)

55. C₂×C₃×C₁₉

C₅²×D₃

direct (N × H)

56. C₂×C₃×C₁₉

C₂×C₃×C₅²

semidirect

57. D₃×C₁₉

C₂×C₃×C₅²

direct (N × H)

59. C₅×C₁₉

C₂×C₃×C₅×D₃

direct (N × H)

60. C₂×C₃²×C₅

C₂×C₅×C₁₉

semidirect

61. C₃×C₅×D₃

C₂×C₅×C₁₉

direct (N × H)

64. C₃×C₅²

C₂×D₃×C₁₉

direct (N × H)

65. C₃×C₅²

C₂²×C₃×C₁₉

semidirect

67. C₂×C₅×D₃

C₃×C₅×C₁₉

direct (N × H)

69. C₃×C₁₉

C₂×C₅²×D₃

direct (N × H)

70. C₃×C₁₉

C₂²×C₃×C₅²

semidirect

72. C₂×C₅²

C₃×D₃×C₁₉

direct (N × H)

73. C₃²×C₅

C₂²×C₅×C₁₉

semidirect

75. C₂×C₁₉

C₃×C₅²×D₃

direct (N × H)

76. C₂×C₃×D₃

C₅²×C₁₉

direct (N × H)

79. C₂×C₃×C₅

C₅×D₃×C₁₉

direct (N × H)

80. C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

semidirect

81. C₅×D₃

C₂×C₃×C₅×C₁₉

direct (N × H)

82. C₅²

C₂×C₃×D₃×C₁₉

direct (N × H)

84. C₁₉

C₂×C₃×C₅²×D₃

direct (N × H)

85. C₂×C₃²

C₂×C₅²×C₁₉

semidirect

86. C₃×D₃

C₂×C₅²×C₁₉

direct (N × H)

88. C₃×C₅

C₂×C₅×D₃×C₁₉

direct (N × H)

89. C₃×C₅

C₂²×C₃×C₅×C₁₉

semidirect

91. C₂×D₃

C₃×C₅²×C₁₉

direct (N × H)

93. C₂×C₅

C₃×C₅×D₃×C₁₉

direct (N × H)

94. C₃²

C₂²×C₅²×C₁₉

semidirect

97. C₂×C₃

C₂×C₃×C₅²×C₁₉

semidirect

98. C₂×C₃

C₅²×D₃×C₁₉

direct (N × H)

99. D₃

C₂×C₃×C₅²×C₁₉

direct (N × H)

100. C₅

C₂×C₃×C₅×D₃×C₁₉

direct (N × H)

103. C₃

C₂²×C₃×C₅²×C₁₉

semidirect

104. C₃

C₂×C₅²×D₃×C₁₉

direct (N × H)

106. C₂

C₃×C₅²×D₃×C₁₉

direct (N × H)

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

subgroup	index
C₃×C₅²×D₃×C₁₉	2
C₂×C₃²×C₅²×C₁₉	2
C₂×C₅²×D₃×C₁₉	3
C₂²×C₃×C₅²×C₁₉	3
C₂×C₃×C₅×D₃×C₁₉	5
C₂×C₃×C₅²×D₃	19

subgroup

index

C₃×C₅²×D₃×C₁₉

C₂×C₃²×C₅²×C₁₉

C₂×C₅²×D₃×C₁₉

C₂²×C₃×C₅²×C₁₉

C₂×C₃×C₅×D₃×C₁₉

C₂×C₃×C₅²×D₃

Subgroups — C₂×C₃×C₅²×D₃×C₁₉ #30685976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C3×C52×D3×C19 #30685976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅²×D₃×C₁₉ #30685976