Group #30685814 — subgroups

Subgroups — D₃×D₁₉×C₅²⋊C₃ #30685814

Order 17100.

128 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 30 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	C₅²⋊C₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×D₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₉×C₅²⋊C₃	—	3	1	no	maximal
6	C₃×C₁₉×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₅²×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₅²×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₉×C₅²⋊C₃	—	3	1	no	—
11	D₁₉×C₅²⋊C₃	—	2	1	no	—
12	D₁₉×C₅²⋊C₃	—	3	1	no	—
13	D₁₉×C₅²⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₅²×D₁₉	—	3	1	no	Hall
15	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₉×C₅²⋊C₃	—	2	1	no	—
17	C₁₉×C₅²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₅×D₃×D₁₉	—	3	2	no	—
19	C₂×C₅²×C₁₉	—	3	1	no	—
20	C₅²×D₁₉	—	3	1	no	—
21	C₅²×D₁₉	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×D₃×C₅²⋊C₃	—	19	1	no	maximal, Hall
23	C₃×D₃×D₁₉	—	25	1	no	maximal, Hall
24	C₅×D₅₇	—	3	2	no	—
25	C₅×D₃×C₁₉	—	3	2	no	—
26	C₃×C₅×D₁₉	—	3	2	no	—
27	C₅²×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₅²⋊C₃	—	19	1	no	—
29	D₃×C₅²⋊C₃	—	19	1	no	—
30	D₃×C₅²⋊C₃	D₁₉	1	1	yes	characteristic, direct product factor
31	C₂×C₅×D₁₉	—	9	2	no	—
32	C₃×D₅₇	—	25	1	no	—
33	C₃×D₃×C₁₉	—	25	1	no	—
34	C₃²×D₁₉	—	25	1	no	—
35	C₂×C₅²×D₃	—	19	1	no	—
36	C₂²×C₅²⋊C₃	—	57	1	no	—
37	C₃×C₅×C₁₉	—	3	2	no	—
38	C₂×C₃×D₁₉	—	75	1	no	—
39	D₃×D₁₉	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
40	C₃×C₅²⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₁₉	—	9	2	no	—
42	C₅×D₁₉	—	3	2	no	—
43	C₅×D₁₉	—	9	2	no	—
44	C₃²×C₁₉	—	25	1	no	Hall
45	C₂×C₃×C₅²	—	19	1	no	—
46	C₅²×D₃	—	19	1	no	—
47	C₅²×D₃	C₃×D₁₉	1	1	yes	characteristic, complemented
48	C₂×C₅²⋊C₃	—	3	1	no	—
49	C₂×C₅²⋊C₃	—	19	1	no	—
50	C₂×C₅²⋊C₃	—	38	1	no	—
51	C₂×C₅²⋊C₃	—	57	1	no	—
52	C₂×C₃×C₁₉	—	75	1	no	—
53	D₅₇	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
54	C₃×D₁₉	—	25	1	no	—
55	C₃×D₁₉	—	50	1	no	—
56	C₃×D₁₉	—	75	1	no	—
57	C₃×D₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
58	D₃×C₁₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
59	C₂²×C₅²	—	57	1	no	Hall
60	C₅×C₁₉	—	3	2	no	—
61	C₂×D₁₉	—	3	1	no	Hall
62	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
63	C₅²⋊C₃	—	2	1	no	—
64	C₅²⋊C₃	D₃×D₁₉	1	1	yes	characteristic, direct product factor
65	C₂×C₅×D₃	—	57	2	no	—
66	C₃×C₁₉	—	25	1	no	—
67	C₃×C₁₉	—	50	1	no	—
68	C₃×C₁₉	C₂²×C₅²⋊C₃	1	1	yes	characteristic, complemented
69	C₂×C₅²	—	3	1	no	—
70	C₂×C₅²	—	19	1	no	—
71	C₂×C₅²	—	57	1	no	—
72	C₂×C₁₉	—	3	1	no	—
73	D₁₉	—	3	1	no	—
74	D₁₉	D₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
75	C₂×C₃×D₃	—	475	1	no	Hall
76	C₂×C₃×C₅	—	57	2	no	—
77	C₅×D₃	—	3	2	no	—
78	C₅×D₃	—	57	2	no	—
79	C₅²	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₅	—	171	2	no	—
81	C₁₉	C₂×D₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₃²	—	475	1	no	—
83	C₃×D₃	—	25	1	no	—
84	C₃×D₃	—	475	1	no	—
85	C₃×C₅	—	3	2	no	—
86	C₂²×C₃	—	1425	1	no	—
87	C₂×D₃	—	19	1	no	—
88	C₂×C₅	—	9	2	no	—
89	C₂×C₅	—	57	2	no	—
90	C₂×C₅	—	171	2	no	—
91	C₃²	—	25	1	no	Sylow
92	C₂×C₃	—	19	1	no	—
93	C₂×C₃	—	75	1	no	—
94	C₂×C₃	—	1425	1	no	—
95	C₂×C₃	—	950	1	no	—
96	C₂×C₃	—	475	1	no	—
97	D₃	—	19	1	no	—
98	D₃	D₁₉×C₅²⋊C₃	1	1	yes	characteristic, direct product factor
99	C₅	—	3	2	no	—
100	C₂²	—	57	1	no	Sylow
101	C₃	—	25	1	no	—
102	C₃	—	50	1	no	—
103	C₃	C₂×D₁₉×C₅²⋊C₃	1	1	yes	characteristic, complemented
104	C₂	—	3	1	no	—
105	C₂	—	19	1	no	—
106	C₂	—	57	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅²⋊C₃×D₅₇

C₂

yes

maximal, characteristic, complemented

D₃×C₁₉×C₅²⋊C₃

C₂

yes

maximal, characteristic, complemented

C₃×D₁₉×C₅²⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅²×D₃×D₁₉

C₃

yes

maximal, characteristic, complemented

C₂×D₁₉×C₅²⋊C₃

—

maximal

C₃×C₁₉×C₅²⋊C₃

C₂²

yes

characteristic, complemented, Hall

C₅²×D₅₇

C₂×C₃

yes

characteristic, complemented

C₅²×D₃×C₁₉

C₂×C₃

yes

characteristic, complemented

C₃×C₅²×D₁₉

C₂×C₃

yes

characteristic, complemented

C₂×C₁₉×C₅²⋊C₃

—

D₁₉×C₅²⋊C₃

—

D₁₉×C₅²⋊C₃

—

D₁₉×C₅²⋊C₃

D₃

yes

characteristic, direct product factor

C₂×C₅²×D₁₉

—

Hall

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic, complemented

C₁₉×C₅²⋊C₃

—

C₁₉×C₅²⋊C₃

C₂×D₃

yes

characteristic, complemented

C₅×D₃×D₁₉

—

C₂×C₅²×C₁₉

—

C₅²×D₁₉

—

C₅²×D₁₉

C₃×D₃

yes

characteristic, complemented

C₂×D₃×C₅²⋊C₃

—

maximal, Hall

C₃×D₃×D₁₉

—

maximal, Hall

C₅×D₅₇

—

C₅×D₃×C₁₉

—

C₃×C₅×D₁₉

—

C₅²×C₁₉

C₂×C₃×D₃

yes

characteristic, complemented, Hall

C₂×C₃×C₅²⋊C₃

—

D₃×C₅²⋊C₃

—

D₃×C₅²⋊C₃

D₁₉

yes

characteristic, direct product factor

C₂×C₅×D₁₉

—

C₃×D₅₇

—

C₃×D₃×C₁₉

—

C₃²×D₁₉

—

C₂×C₅²×D₃

—

C₂²×C₅²⋊C₃

—

C₃×C₅×C₁₉

—

C₂×C₃×D₁₉

—

D₃×D₁₉

C₅²⋊C₃

yes

characteristic, direct product factor

C₃×C₅²⋊C₃

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

C₅×D₁₉

—

C₅×D₁₉

—

C₃²×C₁₉

—

Hall

C₂×C₃×C₅²

—

C₅²×D₃

—

C₅²×D₃

C₃×D₁₉

yes

characteristic, complemented

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₂×C₅²⋊C₃

—

C₂×C₃×C₁₉

—

D₅₇

C₂×C₅²⋊C₃

yes

characteristic, complemented

C₃×D₁₉

—

C₃×D₁₉

—

C₃×D₁₉

—

C₃×D₁₉

C₂×C₅²⋊C₃

yes

characteristic, complemented

D₃×C₁₉

C₂×C₅²⋊C₃

yes

characteristic, complemented

C₂²×C₅²

—

Hall

C₅×C₁₉

—

C₂×D₁₉

—

Hall

C₃×C₅²

C₂×C₃×D₁₉

yes

characteristic, complemented

C₅²⋊C₃

—

C₅²⋊C₃

D₃×D₁₉

yes

characteristic, direct product factor

C₂×C₅×D₃

—

C₃×C₁₉

—

C₃×C₁₉

—

C₃×C₁₉

C₂²×C₅²⋊C₃

yes

characteristic, complemented

C₂×C₅²

—

C₂×C₅²

—

C₂×C₅²

—

C₂×C₁₉

—

D₁₉

—

D₁₉

D₃×C₅²⋊C₃

yes

characteristic, direct product factor

C₂×C₃×D₃

—

475

Hall

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

—

C₅²

C₃×D₃×D₁₉

yes

characteristic, complemented, Sylow

C₂²×C₅

—

171

—

C₁₉

C₂×D₃×C₅²⋊C₃

yes

characteristic, complemented, Sylow

C₂×C₃²

—

475

—

C₃×D₃

—

C₃×D₃

—

475

—

C₃×C₅

—

C₂²×C₃

—

1425

—

C₂×D₃

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

—

171

—

C₃²

—

Sylow

C₂×C₃

—

C₂×C₃

—

C₂×C₃

—

1425

—

C₂×C₃

—

950

—

C₂×C₃

—

475

—

D₃

—

D₃

D₁₉×C₅²⋊C₃

yes

characteristic, direct product factor

C₅

—

100

C₂²

—

Sylow

101

C₃

—

102

C₃

—

103

C₃

C₂×D₁₉×C₅²⋊C₃

yes

characteristic, complemented

104

C₂

—

105

C₂

—

106

C₂

—

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

subgroup

G/H

center, Frattini, hypercenter

C₁

commutator, Fitting, socle, cosocle, hypocenter

C₃×C₅²×C₁₉

C₂²×C₃

LCS

G ▷ C₃×C₅²×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. C₅²⋊C₃×D₅₇	C₂	semidirect
2. D₃×C₁₉×C₅²⋊C₃	C₂	semidirect
3. C₃×D₁₉×C₅²⋊C₃	C₂	semidirect
4. C₅²×D₃×D₁₉	C₃	semidirect
6. C₃×C₁₉×C₅²⋊C₃	C₂²	semidirect
7. C₅²×D₅₇	C₂×C₃	semidirect
8. C₅²×D₃×C₁₉	C₂×C₃	semidirect
9. C₃×C₅²×D₁₉	C₂×C₃	semidirect
13. D₁₉×C₅²⋊C₃	D₃	direct (N × H)
15. C₃×C₅²×C₁₉	C₂²×C₃	semidirect
17. C₁₉×C₅²⋊C₃	C₂×D₃	semidirect
21. C₅²×D₁₉	C₃×D₃	semidirect
27. C₅²×C₁₉	C₂×C₃×D₃	semidirect
30. D₃×C₅²⋊C₃	D₁₉	direct (N × H)
39. D₃×D₁₉	C₅²⋊C₃	direct (N × H)
40. C₃×C₅²⋊C₃	C₂×D₁₉	semidirect
47. C₅²×D₃	C₃×D₁₉	semidirect
53. D₅₇	C₂×C₅²⋊C₃	semidirect
57. C₃×D₁₉	C₂×C₅²⋊C₃	semidirect
58. D₃×C₁₉	C₂×C₅²⋊C₃	semidirect
62. C₃×C₅²	C₂×C₃×D₁₉	semidirect
64. C₅²⋊C₃	D₃×D₁₉	direct (N × H)
68. C₃×C₁₉	C₂²×C₅²⋊C₃	semidirect
74. D₁₉	D₃×C₅²⋊C₃	direct (N × H)
79. C₅²	C₃×D₃×D₁₉	semidirect
81. C₁₉	C₂×D₃×C₅²⋊C₃	semidirect
98. D₃	D₁₉×C₅²⋊C₃	direct (N × H)
103. C₃	C₂×D₁₉×C₅²⋊C₃	semidirect

H ≅ G/N

type

1. C₅²⋊C₃×D₅₇

C₂

semidirect

2. D₃×C₁₉×C₅²⋊C₃

C₂

semidirect

3. C₃×D₁₉×C₅²⋊C₃

C₂

semidirect

4. C₅²×D₃×D₁₉

C₃

semidirect

6. C₃×C₁₉×C₅²⋊C₃

C₂²

semidirect

7. C₅²×D₅₇

C₂×C₃

semidirect

8. C₅²×D₃×C₁₉

C₂×C₃

semidirect

9. C₃×C₅²×D₁₉

C₂×C₃

semidirect

13. D₁₉×C₅²⋊C₃

D₃

direct (N × H)

15. C₃×C₅²×C₁₉

C₂²×C₃

semidirect

17. C₁₉×C₅²⋊C₃

C₂×D₃

semidirect

21. C₅²×D₁₉

C₃×D₃

semidirect

27. C₅²×C₁₉

C₂×C₃×D₃

semidirect

30. D₃×C₅²⋊C₃

D₁₉

direct (N × H)

39. D₃×D₁₉

C₅²⋊C₃

direct (N × H)

40. C₃×C₅²⋊C₃

C₂×D₁₉

semidirect

47. C₅²×D₃

C₃×D₁₉

semidirect

53. D₅₇

C₂×C₅²⋊C₃

semidirect

57. C₃×D₁₉

C₂×C₅²⋊C₃

semidirect

58. D₃×C₁₉

C₂×C₅²⋊C₃

semidirect

62. C₃×C₅²

C₂×C₃×D₁₉

semidirect

64. C₅²⋊C₃

D₃×D₁₉

direct (N × H)

68. C₃×C₁₉

C₂²×C₅²⋊C₃

semidirect

74. D₁₉

D₃×C₅²⋊C₃

direct (N × H)

79. C₅²

C₃×D₃×D₁₉

semidirect

81. C₁₉

C₂×D₃×C₅²⋊C₃

semidirect

98. D₃

D₁₉×C₅²⋊C₃

direct (N × H)

103. C₃

C₂×D₁₉×C₅²⋊C₃

semidirect

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

subgroup	index
C₅²⋊C₃×D₅₇	2
D₃×C₁₉×C₅²⋊C₃	2
C₃×D₁₉×C₅²⋊C₃	2
C₅²×D₃×D₁₉	3
C₂×D₁₉×C₅²⋊C₃	3
C₂×D₃×C₅²⋊C₃	19
C₃×D₃×D₁₉	25

subgroup

index

C₅²⋊C₃×D₅₇

D₃×C₁₉×C₅²⋊C₃

C₃×D₁₉×C₅²⋊C₃

C₅²×D₃×D₁₉

C₂×D₁₉×C₅²⋊C₃

C₂×D₃×C₅²⋊C₃

C₃×D₃×D₁₉

Subgroups — D₃×D₁₉×C₅²⋊C₃ #30685814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×D19×C52⋊C3 #30685814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₉×C₅²⋊C₃ #30685814