Group #30685980 — subgroups

Subgroups — C₂×C₃²×C₅×D₅×C₁₉ #30685980

Order 17100.

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

normal subgroups only

This group has 288 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	C₃²×C₅×D₅×C₁₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₅×C₁₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₅×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×C₅×C₁₉	—	5	1	no	maximal
7	C₃×C₅×D₅×C₁₉	C₂×C₃	1	8	yes	direct product factor
8	C₂×C₃×C₅²×C₁₉	C₂×C₃	1	4	yes	complemented
9	C₂×C₅×D₅×C₁₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃²×C₅×C₁₉	—	2	2	no	—
11	C₂×C₃²×C₅×C₁₉	—	5	2	no	—
12	C₂×C₃²×C₅×C₁₉	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃²×C₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃²×D₅×C₁₉	C₂×C₅	1	2	yes	direct product factor
15	C₃×C₅²×C₁₉	C₂²×C₃	1	4	yes	complemented
16	C₂²×C₃×C₅×C₁₉	—	5	4	no	—
17	C₂×C₃×D₅×C₁₉	C₃×C₅	1	4	yes	direct product factor
18	C₂×C₅²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₅×D₅×C₁₉	C₂×C₃²	1	2	yes	direct product factor
20	C₂×C₃²×C₅×D₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃²×C₅×C₁₉	—	2	2	no	—
22	C₃²×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic, direct product factor
23	C₃²×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂²×C₃²×C₁₉	—	5	1	no	Hall
25	C₂×C₃×C₅×C₁₉	—	2	8	no	—
26	C₂×C₃×C₅×C₁₉	—	5	8	no	—
27	C₂×C₃×C₅×C₁₉	C₃×D₅	1	4	yes	direct product factor
28	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	1	4	yes	complemented
29	C₃×D₅×C₁₉	C₂×C₃×C₅	1	8	yes	direct product factor
30	C₅²×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃²×C₅²	C₂×C₁₉	1	1	yes	characteristic, complemented
32	C₃²×C₅×D₅	C₂×C₁₉	1	2	yes	direct product factor
33	C₂²×C₅×C₁₉	—	5	1	no	—
34	C₂×D₅×C₁₉	C₃²×C₅	1	1	yes	characteristic, direct product factor
35	C₂×C₃²×C₁₉	—	5	2	no	—
36	C₂×C₃²×C₁₉	C₅×D₅	1	1	yes	characteristic, direct product factor
37	C₂×C₃×C₅×D₅	C₃×C₁₉	1	4	yes	direct product factor
38	C₃×C₅×C₁₉	—	2	8	no	—
39	C₃×C₅×C₁₉	C₂×C₃×D₅	1	4	yes	direct product factor
40	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	4	yes	complemented
41	C₂²×C₃×C₁₉	—	5	4	no	—
42	C₃²×C₅²	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₁₉	—	2	2	no	—
44	C₂×C₅×C₁₉	—	5	2	no	—
45	C₂×C₅×C₁₉	C₃²×D₅	1	1	yes	characteristic, direct product factor
46	C₂×C₅×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
47	D₅×C₁₉	C₂×C₃²×C₅	1	2	yes	direct product factor
48	C₂²×C₃²×C₅	—	5	1	no	—
49	C₂×C₃²×D₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
50	C₃²×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₅²	C₂×C₃×C₁₉	1	4	yes	complemented
52	C₃×C₅×D₅	C₂×C₃×C₁₉	1	8	yes	direct product factor
53	C₂×C₃×C₁₉	—	5	8	no	—
54	C₂×C₃×C₁₉	C₃×C₅×D₅	1	4	yes	direct product factor
55	C₂×C₅×D₅	C₃²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
56	C₅×C₁₉	—	2	2	no	—
57	C₅×C₁₉	C₂×C₃²×D₅	1	1	yes	characteristic, direct product factor
58	C₅×C₁₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented
59	C₂×C₃²×C₅	—	2	2	no	—
60	C₂×C₃²×C₅	—	5	2	no	—
61	C₂×C₃²×C₅	D₅×C₁₉	1	1	yes	characteristic, direct product factor
62	C₂×C₃²×C₅	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
63	C₃²×D₅	C₂×C₅×C₁₉	1	2	yes	direct product factor
64	C₂²×C₁₉	—	5	1	no	Hall
65	C₃×C₅²	C₂²×C₃×C₁₉	1	4	yes	complemented
66	C₂²×C₃×C₅	—	5	4	no	—
67	C₂×C₃×D₅	C₃×C₅×C₁₉	1	4	yes	direct product factor
68	C₃×C₁₉	C₂×C₃×C₅×D₅	1	4	yes	direct product factor
69	C₂×C₅²	C₂×C₃²×C₁₉	1	1	yes	characteristic, complemented
70	C₅×D₅	C₂×C₃²×C₁₉	1	2	yes	direct product factor
71	C₃²×C₅	—	2	2	no	—
72	C₃²×C₅	C₂×D₅×C₁₉	1	1	yes	characteristic, direct product factor
73	C₃²×C₅	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented
74	C₂×C₁₉	—	5	2	no	—
75	C₂×C₁₉	C₃²×C₅×D₅	1	1	yes	characteristic, direct product factor
76	C₂²×C₃²	—	5	1	no	Hall
77	C₂×C₃×C₅	—	2	8	no	—
78	C₂×C₃×C₅	—	5	8	no	—
79	C₂×C₃×C₅	C₃×D₅×C₁₉	1	4	yes	direct product factor
80	C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	1	4	yes	complemented
81	C₃×D₅	C₂×C₃×C₅×C₁₉	1	8	yes	direct product factor
82	C₅²	C₂²×C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₅	—	5	1	no	—
84	C₂×D₅	C₃²×C₅×C₁₉	1	1	yes	characteristic, direct product factor
85	C₁₉	C₂×C₃²×C₅×D₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₃²	—	5	2	no	—
87	C₂×C₃²	C₅×D₅×C₁₉	1	1	yes	characteristic, direct product factor
88	C₃×C₅	—	2	8	no	—
89	C₃×C₅	C₂×C₃×D₅×C₁₉	1	4	yes	direct product factor
90	C₃×C₅	C₂²×C₃×C₅×C₁₉	1	4	yes	complemented
91	C₂²×C₃	—	5	4	no	—
92	C₂×C₅	—	2	2	no	—
93	C₂×C₅	—	5	2	no	—
94	C₂×C₅	C₃²×D₅×C₁₉	1	1	yes	characteristic, direct product factor
95	C₂×C₅	C₂×C₃²×C₅×C₁₉	1	1	yes	characteristic, complemented
96	D₅	C₂×C₃²×C₅×C₁₉	1	2	yes	direct product factor
97	C₃²	C₂×C₅×D₅×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃	—	5	8	no	—
99	C₂×C₃	C₃×C₅×D₅×C₁₉	1	4	yes	direct product factor
100	C₅	—	2	2	no	—
101	C₅	C₂²×C₃²×C₅×C₁₉	1	1	yes	characteristic, complemented
102	C₅	C₂×C₃²×D₅×C₁₉	1	1	yes	characteristic, direct product factor
103	C₂²	—	5	1	no	Sylow
104	C₃	C₂×C₃×C₅×D₅×C₁₉	1	4	yes	direct product factor
105	C₂	—	5	2	no	—
106	C₂	C₃²×C₅×D₅×C₁₉	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₅×D₅×C₁₉

C₂

yes

maximal, direct product factor

C₂×C₃²×C₅²×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₅×D₅×C₁₉

C₃

yes

maximal, direct product factor

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₃²×D₅×C₁₉

C₅

yes

maximal, characteristic, direct product factor

C₂²×C₃²×C₅×C₁₉

—

maximal

C₃×C₅×D₅×C₁₉

C₂×C₃

yes

direct product factor

C₂×C₃×C₅²×C₁₉

C₂×C₃

yes

complemented

C₂×C₅×D₅×C₁₉

C₃²

yes

characteristic, direct product factor, Hall

C₂×C₃²×C₅×C₁₉

—

C₂×C₃²×C₅×C₁₉

—

C₂×C₃²×C₅×C₁₉

D₅

yes

characteristic, direct product factor

C₂×C₃²×C₅×C₁₉

C₂×C₅

yes

characteristic, complemented

C₃²×D₅×C₁₉

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₉

C₂²×C₃

yes

complemented

C₂²×C₃×C₅×C₁₉

—

C₂×C₃×D₅×C₁₉

C₃×C₅

yes

direct product factor

C₂×C₅²×C₁₉

C₂×C₃²

yes

characteristic, complemented

C₅×D₅×C₁₉

C₂×C₃²

yes

direct product factor

C₂×C₃²×C₅×D₅

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₃²×C₅×C₁₉

—

C₃²×C₅×C₁₉

C₂×D₅

yes

characteristic, direct product factor

C₃²×C₅×C₁₉

C₂²×C₅

yes

characteristic, complemented

C₂²×C₃²×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₃×D₅

yes

direct product factor

C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

yes

complemented

C₃×D₅×C₁₉

C₂×C₃×C₅

yes

direct product factor

C₅²×C₁₉

C₂²×C₃²

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

C₂×C₁₉

yes

characteristic, complemented

C₃²×C₅×D₅

C₂×C₁₉

yes

direct product factor

C₂²×C₅×C₁₉

—

C₂×D₅×C₁₉

C₃²×C₅

yes

characteristic, direct product factor

C₂×C₃²×C₁₉

—

C₂×C₃²×C₁₉

C₅×D₅

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

C₃×C₁₉

yes

direct product factor

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₃×D₅

yes

direct product factor

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

complemented

C₂²×C₃×C₁₉

—

C₃²×C₅²

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₃²×D₅

yes

characteristic, direct product factor

C₂×C₅×C₁₉

C₂×C₃²×C₅

yes

characteristic, complemented

D₅×C₁₉

C₂×C₃²×C₅

yes

direct product factor

C₂²×C₃²×C₅

—

C₂×C₃²×D₅

C₅×C₁₉

yes

characteristic, direct product factor

C₃²×C₁₉

C₂×C₅×D₅

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅²

C₂×C₃×C₁₉

yes

complemented

C₃×C₅×D₅

C₂×C₃×C₁₉

yes

direct product factor

C₂×C₃×C₁₉

—

C₂×C₃×C₁₉

C₃×C₅×D₅

yes

direct product factor

C₂×C₅×D₅

C₃²×C₁₉

yes

characteristic, direct product factor, Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₃²×D₅

yes

characteristic, direct product factor

C₅×C₁₉

C₂²×C₃²×C₅

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₂×C₃²×C₅

D₅×C₁₉

yes

characteristic, direct product factor

C₂×C₃²×C₅

C₂×C₅×C₁₉

yes

characteristic, complemented

C₃²×D₅

C₂×C₅×C₁₉

yes

direct product factor

C₂²×C₁₉

—

Hall

C₃×C₅²

C₂²×C₃×C₁₉

yes

complemented

C₂²×C₃×C₅

—

C₂×C₃×D₅

C₃×C₅×C₁₉

yes

direct product factor

C₃×C₁₉

C₂×C₃×C₅×D₅

yes

direct product factor

C₂×C₅²

C₂×C₃²×C₁₉

yes

characteristic, complemented

C₅×D₅

C₂×C₃²×C₁₉

yes

direct product factor

C₃²×C₅

—

C₃²×C₅

C₂×D₅×C₁₉

yes

characteristic, direct product factor

C₃²×C₅

C₂²×C₅×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₃²×C₅×D₅

yes

characteristic, direct product factor

C₂²×C₃²

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₃×D₅×C₁₉

yes

direct product factor

C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

yes

complemented

C₃×D₅

C₂×C₃×C₅×C₁₉

yes

direct product factor

C₅²

C₂²×C₃²×C₁₉

yes

characteristic, complemented, Sylow

C₂²×C₅

—

C₂×D₅

C₃²×C₅×C₁₉

yes

characteristic, direct product factor

C₁₉

C₂×C₃²×C₅×D₅

yes

characteristic, direct product factor, Sylow

C₂×C₃²

—

C₂×C₃²

C₅×D₅×C₁₉

yes

characteristic, direct product factor

C₃×C₅

—

C₃×C₅

C₂×C₃×D₅×C₁₉

yes

direct product factor

C₃×C₅

C₂²×C₃×C₅×C₁₉

yes

complemented

C₂²×C₃

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₃²×D₅×C₁₉

yes

characteristic, direct product factor

C₂×C₅

C₂×C₃²×C₅×C₁₉

yes

characteristic, complemented

D₅

C₂×C₃²×C₅×C₁₉

yes

direct product factor

C₃²

C₂×C₅×D₅×C₁₉

yes

characteristic, direct product factor, Sylow

C₂×C₃

—

C₂×C₃

C₃×C₅×D₅×C₁₉

yes

direct product factor

100

C₅

—

101

C₅

C₂²×C₃²×C₅×C₁₉

yes

characteristic, complemented

102

C₅

C₂×C₃²×D₅×C₁₉

yes

characteristic, direct product factor

103

C₂²

—

Sylow

104

C₃

C₂×C₃×C₅×D₅×C₁₉

yes

direct product factor

105

C₂

—

106

C₂

C₃²×C₅×D₅×C₁₉

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅×C₁₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃²×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₅×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₃²×C₅×C₁₉

D₅

commutator, cosocle, hypocenter

C₅

C₂²×C₃²×C₅×C₁₉

Frattini

C₁

Fitting, socle

C₂×C₃²×C₅²×C₁₉

C₂

LCS

G ▷ C₅

UCS

C₁ ◁ C₂×C₃²×C₅×C₁₉

N	H ≅ G/N	type
1. C₃²×C₅×D₅×C₁₉	C₂	direct (N × H)
2. C₂×C₃²×C₅²×C₁₉	C₂	semidirect
3. C₂×C₃×C₅×D₅×C₁₉	C₃	direct (N × H)
4. C₃²×C₅²×C₁₉	C₂²	semidirect
5. C₂×C₃²×D₅×C₁₉	C₅	direct (N × H)
7. C₃×C₅×D₅×C₁₉	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅²×C₁₉	C₂×C₃	semidirect
9. C₂×C₅×D₅×C₁₉	C₃²	direct (N × H)
12. C₂×C₃²×C₅×C₁₉	D₅	direct (N × H)
13. C₂×C₃²×C₅×C₁₉	C₂×C₅	semidirect
14. C₃²×D₅×C₁₉	C₂×C₅	direct (N × H)
15. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
17. C₂×C₃×D₅×C₁₉	C₃×C₅	direct (N × H)
18. C₂×C₅²×C₁₉	C₂×C₃²	semidirect
19. C₅×D₅×C₁₉	C₂×C₃²	direct (N × H)
20. C₂×C₃²×C₅×D₅	C₁₉	direct (N × H)
22. C₃²×C₅×C₁₉	C₂×D₅	direct (N × H)
23. C₃²×C₅×C₁₉	C₂²×C₅	semidirect
27. C₂×C₃×C₅×C₁₉	C₃×D₅	direct (N × H)
28. C₂×C₃×C₅×C₁₉	C₂×C₃×C₅	semidirect
29. C₃×D₅×C₁₉	C₂×C₃×C₅	direct (N × H)
30. C₅²×C₁₉	C₂²×C₃²	semidirect
31. C₂×C₃²×C₅²	C₂×C₁₉	semidirect
32. C₃²×C₅×D₅	C₂×C₁₉	direct (N × H)
34. C₂×D₅×C₁₉	C₃²×C₅	direct (N × H)
36. C₂×C₃²×C₁₉	C₅×D₅	direct (N × H)
37. C₂×C₃×C₅×D₅	C₃×C₁₉	direct (N × H)
39. C₃×C₅×C₁₉	C₂×C₃×D₅	direct (N × H)
40. C₃×C₅×C₁₉	C₂²×C₃×C₅	semidirect
42. C₃²×C₅²	C₂²×C₁₉	semidirect
45. C₂×C₅×C₁₉	C₃²×D₅	direct (N × H)
46. C₂×C₅×C₁₉	C₂×C₃²×C₅	semidirect
47. D₅×C₁₉	C₂×C₃²×C₅	direct (N × H)
49. C₂×C₃²×D₅	C₅×C₁₉	direct (N × H)
50. C₃²×C₁₉	C₂×C₅×D₅	direct (N × H)
51. C₂×C₃×C₅²	C₂×C₃×C₁₉	semidirect
52. C₃×C₅×D₅	C₂×C₃×C₁₉	direct (N × H)
54. C₂×C₃×C₁₉	C₃×C₅×D₅	direct (N × H)
55. C₂×C₅×D₅	C₃²×C₁₉	direct (N × H)
57. C₅×C₁₉	C₂×C₃²×D₅	direct (N × H)
58. C₅×C₁₉	C₂²×C₃²×C₅	semidirect
61. C₂×C₃²×C₅	D₅×C₁₉	direct (N × H)
62. C₂×C₃²×C₅	C₂×C₅×C₁₉	semidirect
63. C₃²×D₅	C₂×C₅×C₁₉	direct (N × H)
65. C₃×C₅²	C₂²×C₃×C₁₉	semidirect
67. C₂×C₃×D₅	C₃×C₅×C₁₉	direct (N × H)
68. C₃×C₁₉	C₂×C₃×C₅×D₅	direct (N × H)
69. C₂×C₅²	C₂×C₃²×C₁₉	semidirect
70. C₅×D₅	C₂×C₃²×C₁₉	direct (N × H)
72. C₃²×C₅	C₂×D₅×C₁₉	direct (N × H)
73. C₃²×C₅	C₂²×C₅×C₁₉	semidirect
75. C₂×C₁₉	C₃²×C₅×D₅	direct (N × H)
79. C₂×C₃×C₅	C₃×D₅×C₁₉	direct (N × H)
80. C₂×C₃×C₅	C₂×C₃×C₅×C₁₉	semidirect
81. C₃×D₅	C₂×C₃×C₅×C₁₉	direct (N × H)
82. C₅²	C₂²×C₃²×C₁₉	semidirect
84. C₂×D₅	C₃²×C₅×C₁₉	direct (N × H)
85. C₁₉	C₂×C₃²×C₅×D₅	direct (N × H)
87. C₂×C₃²	C₅×D₅×C₁₉	direct (N × H)
89. C₃×C₅	C₂×C₃×D₅×C₁₉	direct (N × H)
90. C₃×C₅	C₂²×C₃×C₅×C₁₉	semidirect
94. C₂×C₅	C₃²×D₅×C₁₉	direct (N × H)
95. C₂×C₅	C₂×C₃²×C₅×C₁₉	semidirect
96. D₅	C₂×C₃²×C₅×C₁₉	direct (N × H)
97. C₃²	C₂×C₅×D₅×C₁₉	direct (N × H)
99. C₂×C₃	C₃×C₅×D₅×C₁₉	direct (N × H)
101. C₅	C₂²×C₃²×C₅×C₁₉	semidirect
102. C₅	C₂×C₃²×D₅×C₁₉	direct (N × H)
104. C₃	C₂×C₃×C₅×D₅×C₁₉	direct (N × H)
106. C₂	C₃²×C₅×D₅×C₁₉	direct (N × H)

H ≅ G/N

type

1. C₃²×C₅×D₅×C₁₉

C₂

direct (N × H)

2. C₂×C₃²×C₅²×C₁₉

C₂

semidirect

3. C₂×C₃×C₅×D₅×C₁₉

C₃

direct (N × H)

4. C₃²×C₅²×C₁₉

C₂²

semidirect

5. C₂×C₃²×D₅×C₁₉

C₅

direct (N × H)

7. C₃×C₅×D₅×C₁₉

C₂×C₃

direct (N × H)

8. C₂×C₃×C₅²×C₁₉

C₂×C₃

semidirect

9. C₂×C₅×D₅×C₁₉

C₃²

direct (N × H)

12. C₂×C₃²×C₅×C₁₉

D₅

direct (N × H)

13. C₂×C₃²×C₅×C₁₉

C₂×C₅

semidirect

14. C₃²×D₅×C₁₉

C₂×C₅

direct (N × H)

15. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

17. C₂×C₃×D₅×C₁₉

C₃×C₅

direct (N × H)

18. C₂×C₅²×C₁₉

C₂×C₃²

semidirect

19. C₅×D₅×C₁₉

C₂×C₃²

direct (N × H)

20. C₂×C₃²×C₅×D₅

C₁₉

direct (N × H)

22. C₃²×C₅×C₁₉

C₂×D₅

direct (N × H)

23. C₃²×C₅×C₁₉

C₂²×C₅

semidirect

27. C₂×C₃×C₅×C₁₉

C₃×D₅

direct (N × H)

28. C₂×C₃×C₅×C₁₉

C₂×C₃×C₅

semidirect

29. C₃×D₅×C₁₉

C₂×C₃×C₅

direct (N × H)

30. C₅²×C₁₉

C₂²×C₃²

semidirect

31. C₂×C₃²×C₅²

C₂×C₁₉

semidirect

32. C₃²×C₅×D₅

C₂×C₁₉

direct (N × H)

34. C₂×D₅×C₁₉

C₃²×C₅

direct (N × H)

36. C₂×C₃²×C₁₉

C₅×D₅

direct (N × H)

37. C₂×C₃×C₅×D₅

C₃×C₁₉

direct (N × H)

39. C₃×C₅×C₁₉

C₂×C₃×D₅

direct (N × H)

40. C₃×C₅×C₁₉

C₂²×C₃×C₅

semidirect

42. C₃²×C₅²

C₂²×C₁₉

semidirect

45. C₂×C₅×C₁₉

C₃²×D₅

direct (N × H)

46. C₂×C₅×C₁₉

C₂×C₃²×C₅

semidirect

47. D₅×C₁₉

C₂×C₃²×C₅

direct (N × H)

49. C₂×C₃²×D₅

C₅×C₁₉

direct (N × H)

50. C₃²×C₁₉

C₂×C₅×D₅

direct (N × H)

51. C₂×C₃×C₅²

C₂×C₃×C₁₉

semidirect

52. C₃×C₅×D₅

C₂×C₃×C₁₉

direct (N × H)

54. C₂×C₃×C₁₉

C₃×C₅×D₅

direct (N × H)

55. C₂×C₅×D₅

C₃²×C₁₉

direct (N × H)

57. C₅×C₁₉

C₂×C₃²×D₅

direct (N × H)

58. C₅×C₁₉

C₂²×C₃²×C₅

semidirect

61. C₂×C₃²×C₅

D₅×C₁₉

direct (N × H)

62. C₂×C₃²×C₅

C₂×C₅×C₁₉

semidirect

63. C₃²×D₅

C₂×C₅×C₁₉

direct (N × H)

65. C₃×C₅²

C₂²×C₃×C₁₉

semidirect

67. C₂×C₃×D₅

C₃×C₅×C₁₉

direct (N × H)

68. C₃×C₁₉

C₂×C₃×C₅×D₅

direct (N × H)

69. C₂×C₅²

C₂×C₃²×C₁₉

semidirect

70. C₅×D₅

C₂×C₃²×C₁₉

direct (N × H)

72. C₃²×C₅

C₂×D₅×C₁₉

direct (N × H)

73. C₃²×C₅

C₂²×C₅×C₁₉

semidirect

75. C₂×C₁₉

C₃²×C₅×D₅

direct (N × H)

79. C₂×C₃×C₅

C₃×D₅×C₁₉

direct (N × H)

80. C₂×C₃×C₅

C₂×C₃×C₅×C₁₉

semidirect

81. C₃×D₅

C₂×C₃×C₅×C₁₉

direct (N × H)

82. C₅²

C₂²×C₃²×C₁₉

semidirect

84. C₂×D₅

C₃²×C₅×C₁₉

direct (N × H)

85. C₁₉

C₂×C₃²×C₅×D₅

direct (N × H)

87. C₂×C₃²

C₅×D₅×C₁₉

direct (N × H)

89. C₃×C₅

C₂×C₃×D₅×C₁₉

direct (N × H)

90. C₃×C₅

C₂²×C₃×C₅×C₁₉

semidirect

94. C₂×C₅

C₃²×D₅×C₁₉

direct (N × H)

95. C₂×C₅

C₂×C₃²×C₅×C₁₉

semidirect

96. D₅

C₂×C₃²×C₅×C₁₉

direct (N × H)

97. C₃²

C₂×C₅×D₅×C₁₉

direct (N × H)

99. C₂×C₃

C₃×C₅×D₅×C₁₉

direct (N × H)

101. C₅

C₂²×C₃²×C₅×C₁₉

semidirect

102. C₅

C₂×C₃²×D₅×C₁₉

direct (N × H)

104. C₃

C₂×C₃×C₅×D₅×C₁₉

direct (N × H)

106. C₂

C₃²×C₅×D₅×C₁₉

direct (N × H)

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

subgroup	index
C₃²×C₅×D₅×C₁₉	2
C₂×C₃²×C₅²×C₁₉	2
C₂×C₃×C₅×D₅×C₁₉	3
C₂×C₃²×D₅×C₁₉	5
C₂²×C₃²×C₅×C₁₉	5
C₂×C₃²×C₅×D₅	19

subgroup

index

C₃²×C₅×D₅×C₁₉

C₂×C₃²×C₅²×C₁₉

C₂×C₃×C₅×D₅×C₁₉

C₂×C₃²×D₅×C₁₉

C₂²×C₃²×C₅×C₁₉

C₂×C₃²×C₅×D₅

Subgroups — C₂×C₃²×C₅×D₅×C₁₉ #30685980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C32×C5×D5×C19 #30685980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×D₅×C₁₉ #30685980