Group #30685625 — subgroups

Subgroups — C₂×C₅×C₁₉×D₄₅ #30685625

Order 17100.

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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	C₅×C₁₉×D₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₉×D₁₅	—	3	1	no	maximal
4	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×D₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₅×D₉×C₁₉	—	5	1	no	maximal
7	C₅×C₁₉×D₁₅	—	3	2	no	—
8	C₂×C₃×C₅²×C₁₉	D₃	1	1	yes	characteristic
9	C₂×C₅×D₅×C₁₉	—	9	1	no	Hall
10	C₂×C₅×C₉×C₁₉	—	2	2	no	—
11	C₂×C₅×C₉×C₁₉	D₅	1	1	yes	characteristic, complemented
12	C₂×C₅×C₉×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₁₉×D₄₅	C₂×C₅	1	2	yes	direct product factor
14	C₅×D₉×C₁₉	—	5	2	no	—
15	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
16	C₂×C₁₉×D₁₅	—	3	1	no	—
17	C₂×C₅×D₃×C₁₉	—	15	1	no	—
18	C₂×C₅²×C₁₉	D₉	1	1	yes	characteristic, complemented
19	C₅×D₅×C₁₉	—	9	2	no	—
20	C₂×C₅×D₄₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₅×C₉×C₁₉	—	2	2	no	—
22	C₅×C₉×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
23	C₅×C₉×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂×D₉×C₁₉	—	5	1	no	Hall
25	C₂×C₃×C₅×C₁₉	—	2	2	no	—
26	C₂×C₃×C₅×C₁₉	C₅×D₃	1	1	yes	characteristic
27	C₂×C₃×C₅×C₁₉	D₁₅	1	1	yes	characteristic
28	C₁₉×D₁₅	—	3	2	no	—
29	C₅×D₃×C₁₉	—	15	2	no	—
30	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²×C₉	C₂×C₁₉	1	1	yes	characteristic, complemented
32	C₅×D₄₅	C₂×C₁₉	1	2	yes	direct product factor
33	C₂²×C₅×C₁₉	—	45	1	no	—
34	C₂×D₅×C₁₉	—	9	1	no	—
35	C₂×C₉×C₁₉	C₅×D₅	1	1	yes	characteristic, complemented
36	D₉×C₁₉	—	5	2	no	—
37	C₂×C₅×D₁₅	—	3	1	no	—
38	C₃×C₅×C₁₉	—	2	2	no	—
39	C₃×C₅×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic
40	C₃×C₅×C₁₉	C₂×D₁₅	1	1	yes	characteristic
41	C₂×D₃×C₁₉	—	15	1	no	—
42	C₅²×C₉	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
43	C₂×C₅×C₁₉	—	2	2	no	—
44	C₂×C₅×C₁₉	—	45	2	no	—
45	C₂×C₅×C₁₉	C₅×D₉	1	1	yes	characteristic, complemented
46	C₂×C₅×C₁₉	D₄₅	1	1	yes	characteristic, direct product factor
47	D₅×C₁₉	—	9	2	no	—
48	C₂×D₄₅	C₅×C₁₉	1	1	yes	characteristic, direct product factor
49	C₂×C₅×D₉	—	5	1	no	—
50	C₉×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₅²	D₃×C₁₉	1	1	yes	characteristic
52	C₅×D₁₅	—	3	2	no	—
53	C₂×C₃×C₁₉	C₅×D₁₅	1	1	yes	characteristic
54	D₃×C₁₉	—	15	2	no	—
55	C₂×C₅×D₅	—	9	1	no	Hall
56	C₅×C₁₉	—	2	2	no	—
57	C₅×C₁₉	C₂×C₅×D₉	1	1	yes	characteristic, complemented
58	C₅×C₁₉	C₂×D₄₅	1	1	yes	characteristic, direct product factor
59	C₂×C₅×C₉	—	2	2	no	—
60	C₂×C₅×C₉	D₅×C₁₉	1	1	yes	characteristic, complemented
61	C₂×C₅×C₉	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
62	D₄₅	C₂×C₅×C₁₉	1	2	yes	direct product factor
63	C₅×D₉	—	5	2	no	—
64	C₂²×C₁₉	—	45	1	no	Hall
65	C₃×C₅²	C₂×D₃×C₁₉	1	1	yes	characteristic
66	C₂×D₁₅	—	3	1	no	—
67	C₂×C₅×D₃	—	15	1	no	—
68	C₃×C₁₉	C₂×C₅×D₁₅	1	1	yes	characteristic
69	C₂×C₅²	D₉×C₁₉	1	1	yes	characteristic, complemented
70	C₅×D₅	—	9	2	no	—
71	C₅×C₉	—	2	2	no	—
72	C₅×C₉	C₂×D₅×C₁₉	1	1	yes	characteristic, complemented
73	C₅×C₉	C₂²×C₅×C₁₉	1	1	yes	characteristic, complemented
74	C₂×C₁₉	—	45	2	no	—
75	C₂×C₁₉	C₅×D₄₅	1	1	yes	characteristic, direct product factor
76	C₂×D₉	—	5	1	no	Hall
77	C₂×C₃×C₅	—	2	2	no	—
78	C₂×C₃×C₅	C₅×D₃×C₁₉	1	1	yes	characteristic
79	C₂×C₃×C₅	C₁₉×D₁₅	1	1	yes	characteristic
80	D₁₅	—	3	2	no	—
81	C₅×D₃	—	15	2	no	—
82	C₅²	C₂×D₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₅	—	45	1	no	—
84	C₂×D₅	—	9	1	no	—
85	C₁₉	C₂×C₅×D₄₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₉	C₅×D₅×C₁₉	1	1	yes	characteristic, complemented
87	D₉	—	5	2	no	—
88	C₃×C₅	—	2	2	no	—
89	C₃×C₅	C₂×C₅×D₃×C₁₉	1	1	yes	characteristic
90	C₃×C₅	C₂×C₁₉×D₁₅	1	1	yes	characteristic
91	C₂×D₃	—	15	1	no	—
92	C₂×C₅	—	2	2	no	—
93	C₂×C₅	—	45	2	no	—
94	C₂×C₅	C₅×D₉×C₁₉	1	1	yes	characteristic, complemented
95	C₂×C₅	C₁₉×D₄₅	1	1	yes	characteristic, direct product factor
96	D₅	—	9	2	no	—
97	C₉	C₂×C₅×D₅×C₁₉	1	1	yes	characteristic, complemented, Sylow
98	C₂×C₃	C₅×C₁₉×D₁₅	1	1	yes	characteristic
99	D₃	—	15	2	no	—
100	C₅	—	2	2	no	—
101	C₅	C₂×C₅×D₉×C₁₉	1	1	yes	characteristic, complemented
102	C₅	C₂×C₁₉×D₄₅	1	1	yes	characteristic, direct product factor
103	C₂²	—	45	1	no	Sylow
104	C₃	C₂×C₅×C₁₉×D₁₅	1	1	yes	characteristic
105	C₂	—	45	2	no	—
106	C₂	C₅×C₁₉×D₄₅	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₁₉×D₄₅

C₂

yes

maximal, direct product factor

C₂×C₅²×C₉×C₁₉

C₂

yes

maximal, characteristic, complemented

C₂×C₅×C₁₉×D₁₅

—

maximal

C₅²×C₉×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₁₉×D₄₅

C₅

yes

maximal, characteristic, direct product factor

C₂×C₅×D₉×C₁₉

—

maximal

C₅×C₁₉×D₁₅

—

C₂×C₃×C₅²×C₁₉

D₃

yes

characteristic

C₂×C₅×D₅×C₁₉

—

Hall

C₂×C₅×C₉×C₁₉

—

C₂×C₅×C₉×C₁₉

D₅

yes

characteristic, complemented

C₂×C₅×C₉×C₁₉

C₂×C₅

yes

characteristic, complemented

C₁₉×D₄₅

C₂×C₅

yes

direct product factor

C₅×D₉×C₁₉

—

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic

C₂×C₁₉×D₁₅

—

C₂×C₅×D₃×C₁₉

—

C₂×C₅²×C₁₉

D₉

yes

characteristic, complemented

C₅×D₅×C₁₉

—

C₂×C₅×D₄₅

C₁₉

yes

maximal, characteristic, direct product factor, Hall

C₅×C₉×C₁₉

—

C₅×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented

C₅×C₉×C₁₉

C₂²×C₅

yes

characteristic, complemented

C₂×D₉×C₁₉

—

Hall

C₂×C₃×C₅×C₁₉

—

C₂×C₃×C₅×C₁₉

C₅×D₃

yes

characteristic

C₂×C₃×C₅×C₁₉

D₁₅

yes

characteristic

C₁₉×D₁₅

—

C₅×D₃×C₁₉

—

C₅²×C₁₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂×C₅²×C₉

C₂×C₁₉

yes

characteristic, complemented

C₅×D₄₅

C₂×C₁₉

yes

direct product factor

C₂²×C₅×C₁₉

—

C₂×D₅×C₁₉

—

C₂×C₉×C₁₉

C₅×D₅

yes

characteristic, complemented

D₉×C₁₉

—

C₂×C₅×D₁₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

characteristic

C₃×C₅×C₁₉

C₂×D₁₅

yes

characteristic

C₂×D₃×C₁₉

—

C₅²×C₉

C₂²×C₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

—

C₂×C₅×C₁₉

C₅×D₉

yes

characteristic, complemented

C₂×C₅×C₁₉

D₄₅

yes

characteristic, direct product factor

D₅×C₁₉

—

C₂×D₄₅

C₅×C₁₉

yes

characteristic, direct product factor

C₂×C₅×D₉

—

C₉×C₁₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

D₃×C₁₉

yes

characteristic

C₅×D₁₅

—

C₂×C₃×C₁₉

C₅×D₁₅

yes

characteristic

D₃×C₁₉

—

C₂×C₅×D₅

—

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₅×D₉

yes

characteristic, complemented

C₅×C₁₉

C₂×D₄₅

yes

characteristic, direct product factor

C₂×C₅×C₉

—

C₂×C₅×C₉

D₅×C₁₉

yes

characteristic, complemented

C₂×C₅×C₉

C₂×C₅×C₁₉

yes

characteristic, complemented

D₄₅

C₂×C₅×C₁₉

yes

direct product factor

C₅×D₉

—

C₂²×C₁₉

—

Hall

C₃×C₅²

C₂×D₃×C₁₉

yes

characteristic

C₂×D₁₅

—

C₂×C₅×D₃

—

C₃×C₁₉

C₂×C₅×D₁₅

yes

characteristic

C₂×C₅²

D₉×C₁₉

yes

characteristic, complemented

C₅×D₅

—

C₅×C₉

—

C₅×C₉

C₂×D₅×C₁₉

yes

characteristic, complemented

C₅×C₉

C₂²×C₅×C₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

C₅×D₄₅

yes

characteristic, direct product factor

C₂×D₉

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

C₅×D₃×C₁₉

yes

characteristic

C₂×C₃×C₅

C₁₉×D₁₅

yes

characteristic

D₁₅

—

C₅×D₃

—

C₅²

C₂×D₉×C₁₉

yes

characteristic, complemented, Sylow

C₂²×C₅

—

C₂×D₅

—

C₁₉

C₂×C₅×D₄₅

yes

characteristic, direct product factor, Sylow

C₂×C₉

C₅×D₅×C₁₉

yes

characteristic, complemented

D₉

—

C₃×C₅

—

C₃×C₅

C₂×C₅×D₃×C₁₉

yes

characteristic

C₃×C₅

C₂×C₁₉×D₁₅

yes

characteristic

C₂×D₃

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₅×D₉×C₁₉

yes

characteristic, complemented

C₂×C₅

C₁₉×D₄₅

yes

characteristic, direct product factor

D₅

—

C₉

C₂×C₅×D₅×C₁₉

yes

characteristic, complemented, Sylow

C₂×C₃

C₅×C₁₉×D₁₅

yes

characteristic

D₃

—

100

C₅

—

101

C₅

C₂×C₅×D₉×C₁₉

yes

characteristic, complemented

102

C₅

C₂×C₁₉×D₄₅

yes

characteristic, direct product factor

103

C₂²

—

Sylow

104

C₃

C₂×C₅×C₁₉×D₁₅

yes

characteristic

105

C₂

—

106

C₂

C₅×C₁₉×D₄₅

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₅×C₁₉
Frattini	C₃	C₂×C₅×C₁₉×D₁₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle	C₂×C₃×C₅²×C₁₉	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂×C₅×C₁₉

subgroup

G/H

center, hypercenter

C₂×C₅×C₁₉

D₄₅

commutator, cosocle, hypocenter

C₅×C₉

C₂²×C₅×C₁₉

Frattini

C₃

C₂×C₅×C₁₉×D₁₅

Fitting

C₂×C₅²×C₉×C₁₉

C₂

socle

C₂×C₃×C₅²×C₁₉

D₃

LCS

G ▷ C₅×C₉

UCS

C₁ ◁ C₂×C₅×C₁₉

N	H ≅ G/N	type
1. C₅×C₁₉×D₄₅	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₉	C₂	semidirect
4. C₅²×C₉×C₁₉	C₂²	semidirect
5. C₂×C₁₉×D₄₅	C₅	direct (N × H)
11. C₂×C₅×C₉×C₁₉	D₅	semidirect
12. C₂×C₅×C₉×C₁₉	C₂×C₅	semidirect
13. C₁₉×D₄₅	C₂×C₅	direct (N × H)
18. C₂×C₅²×C₁₉	D₉	semidirect
20. C₂×C₅×D₄₅	C₁₉	direct (N × H)
22. C₅×C₉×C₁₉	C₂×D₅	semidirect
23. C₅×C₉×C₁₉	C₂²×C₅	semidirect
30. C₅²×C₁₉	C₂×D₉	semidirect
31. C₂×C₅²×C₉	C₂×C₁₉	semidirect
32. C₅×D₄₅	C₂×C₁₉	direct (N × H)
35. C₂×C₉×C₁₉	C₅×D₅	semidirect
42. C₅²×C₉	C₂²×C₁₉	semidirect
45. C₂×C₅×C₁₉	C₅×D₉	semidirect
46. C₂×C₅×C₁₉	D₄₅	direct (N × H)
48. C₂×D₄₅	C₅×C₁₉	direct (N × H)
50. C₉×C₁₉	C₂×C₅×D₅	semidirect
57. C₅×C₁₉	C₂×C₅×D₉	semidirect
58. C₅×C₁₉	C₂×D₄₅	direct (N × H)
60. C₂×C₅×C₉	D₅×C₁₉	semidirect
61. C₂×C₅×C₉	C₂×C₅×C₁₉	semidirect
62. D₄₅	C₂×C₅×C₁₉	direct (N × H)
69. C₂×C₅²	D₉×C₁₉	semidirect
72. C₅×C₉	C₂×D₅×C₁₉	semidirect
73. C₅×C₉	C₂²×C₅×C₁₉	semidirect
75. C₂×C₁₉	C₅×D₄₅	direct (N × H)
82. C₅²	C₂×D₉×C₁₉	semidirect
85. C₁₉	C₂×C₅×D₄₅	direct (N × H)
86. C₂×C₉	C₅×D₅×C₁₉	semidirect
94. C₂×C₅	C₅×D₉×C₁₉	semidirect
95. C₂×C₅	C₁₉×D₄₅	direct (N × H)
97. C₉	C₂×C₅×D₅×C₁₉	semidirect
101. C₅	C₂×C₅×D₉×C₁₉	semidirect
102. C₅	C₂×C₁₉×D₄₅	direct (N × H)
106. C₂	C₅×C₁₉×D₄₅	direct (N × H)

H ≅ G/N

type

1. C₅×C₁₉×D₄₅

C₂

direct (N × H)

2. C₂×C₅²×C₉×C₁₉

C₂

semidirect

4. C₅²×C₉×C₁₉

C₂²

semidirect

5. C₂×C₁₉×D₄₅

C₅

direct (N × H)

11. C₂×C₅×C₉×C₁₉

D₅

semidirect

12. C₂×C₅×C₉×C₁₉

C₂×C₅

semidirect

13. C₁₉×D₄₅

C₂×C₅

direct (N × H)

18. C₂×C₅²×C₁₉

D₉

semidirect

20. C₂×C₅×D₄₅

C₁₉

direct (N × H)

22. C₅×C₉×C₁₉

C₂×D₅

semidirect

23. C₅×C₉×C₁₉

C₂²×C₅

semidirect

30. C₅²×C₁₉

C₂×D₉

semidirect

31. C₂×C₅²×C₉

C₂×C₁₉

semidirect

32. C₅×D₄₅

C₂×C₁₉

direct (N × H)

35. C₂×C₉×C₁₉

C₅×D₅

semidirect

42. C₅²×C₉

C₂²×C₁₉

semidirect

45. C₂×C₅×C₁₉

C₅×D₉

semidirect

46. C₂×C₅×C₁₉

D₄₅

direct (N × H)

48. C₂×D₄₅

C₅×C₁₉

direct (N × H)

50. C₉×C₁₉

C₂×C₅×D₅

semidirect

57. C₅×C₁₉

C₂×C₅×D₉

semidirect

58. C₅×C₁₉

C₂×D₄₅

direct (N × H)

60. C₂×C₅×C₉

D₅×C₁₉

semidirect

61. C₂×C₅×C₉

C₂×C₅×C₁₉

semidirect

62. D₄₅

C₂×C₅×C₁₉

direct (N × H)

69. C₂×C₅²

D₉×C₁₉

semidirect

72. C₅×C₉

C₂×D₅×C₁₉

semidirect

73. C₅×C₉

C₂²×C₅×C₁₉

semidirect

75. C₂×C₁₉

C₅×D₄₅

direct (N × H)

82. C₅²

C₂×D₉×C₁₉

semidirect

85. C₁₉

C₂×C₅×D₄₅

direct (N × H)

86. C₂×C₉

C₅×D₅×C₁₉

semidirect

94. C₂×C₅

C₅×D₉×C₁₉

semidirect

95. C₂×C₅

C₁₉×D₄₅

direct (N × H)

97. C₉

C₂×C₅×D₅×C₁₉

semidirect

101. C₅

C₂×C₅×D₉×C₁₉

semidirect

102. C₅

C₂×C₁₉×D₄₅

direct (N × H)

106. C₂

C₅×C₁₉×D₄₅

direct (N × H)

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

subgroup	index
C₅×C₁₉×D₄₅	2
C₂×C₅²×C₉×C₁₉	2
C₂×C₅×C₁₉×D₁₅	3
C₂×C₁₉×D₄₅	5
C₂×C₅×D₉×C₁₉	5
C₂×C₅×D₄₅	19

subgroup

index

C₅×C₁₉×D₄₅

C₂×C₅²×C₉×C₁₉

C₂×C₅×C₁₉×D₁₅

C₂×C₁₉×D₄₅

C₂×C₅×D₉×C₁₉

C₂×C₅×D₄₅

Subgroups — C₂×C₅×C₁₉×D₄₅ #30685625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×C19×D45 #30685625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₉×D₄₅ #30685625