Group #44570540 — subgroups

Subgroups — C₁₉⋊C₃×C₅⋊(D₁₉⋊C₃) #44570540

Order 32490.

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

normal subgroups only

This group has 108 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	C₅×C₁₉⋊C₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉⋊C₃×D₉₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#14524209	C₃	1	1	yes	maximal, characteristic, complemented
4	C₅⋊#14524208	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₉×C₅⋊(D₁₉⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₉⋊C₃×D₁₉⋊C₃	—	5	1	no	maximal, Hall
7	C₅×#11762246	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅×#11762245	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₁₉×D₉₅	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₁₉⋊C₃²	D₅	1	1	yes	characteristic, complemented, Hall
13	D₁₉×C₁₉⋊C₃	—	5	1	no	—
14	#14524209	—	5	1	no	—
15	#14524208	—	5	1	no	—
16	C₁₉×D₁₉⋊C₃	—	5	1	no	—
17	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅⋊(D₁₉⋊C₃)	—	19	1	no	maximal
19	C₃×D₅×C₁₉⋊C₃	—	19	1	no	maximal
20	#11762246	C₃×D₅	1	1	yes	characteristic, complemented
21	#11762245	C₃×D₅	1	1	yes	characteristic, complemented
22	C₁₉×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic, complemented
23	C₁₉×C₁₉⋊C₃	C₃×D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
25	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
26	C₁₉×D₁₉	—	5	1	no	Hall
27	C₃×D₉₅	—	19	1	no	—
28	C₃×D₅×C₁₉	—	19	1	no	—
29	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
30	C₅⋊(D₁₉⋊C₃)	—	19	1	no	—
31	C₅⋊(D₁₉⋊C₃)	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
32	D₅×C₁₉⋊C₃	—	19	1	no	—
33	D₅×C₁₉⋊C₃	—	19	1	no	—
34	D₅×C₁₉⋊C₃	—	19	1	no	—
35	C₁₉²	C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₉⋊C₃	—	95	1	no	—
37	C₃×D₁₉⋊C₃	—	95	1	no	—
38	C₃×C₅×C₁₉	—	19	1	no	—
39	C₃×C₅×C₁₉	—	19	1	no	—
40	C₅×C₁₉⋊C₃	—	19	1	no	—
41	C₅×C₁₉⋊C₃	—	19	1	no	—
42	C₅×C₁₉⋊C₃	—	19	1	no	—
43	C₅×C₁₉⋊C₃	—	19	1	no	—
44	C₅×C₁₉⋊C₃	—	114	3	no	—
45	C₅×C₁₉⋊C₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented
46	C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	D₉₅	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
48	D₅×C₁₉	—	19	1	no	—
49	C₃×C₁₉⋊C₃	—	19	1	no	—
50	C₃×C₁₉⋊C₃	—	19	1	no	—
51	C₂×C₃×C₁₉	—	95	1	no	—
52	C₃×D₁₉	—	95	1	no	—
53	C₂×C₁₉⋊C₃	—	95	1	no	—
54	C₂×C₁₉⋊C₃	—	95	1	no	—
55	C₂×C₁₉⋊C₃	—	95	1	no	—
56	D₁₉⋊C₃	—	5	1	no	—
57	D₁₉⋊C₃	—	95	1	no	—
58	D₁₉⋊C₃	—	95	1	no	—
59	C₅×C₁₉	—	6	3	no	—
60	C₅×C₁₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
61	C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
62	C₃²×D₅	—	361	1	no	Hall
63	C₃×C₁₉	—	19	1	no	—
64	C₃×C₁₉	—	19	1	no	—
65	C₁₉⋊C₃	—	19	1	no	—
66	C₁₉⋊C₃	—	19	1	no	—
67	C₁₉⋊C₃	—	19	1	no	—
68	C₁₉⋊C₃	—	19	1	no	—
69	C₁₉⋊C₃	—	114	3	no	—
70	C₁₉⋊C₃	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
71	C₁₉⋊C₃	C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
72	C₃²×C₅	—	361	1	no	Hall
73	C₂×C₁₉	—	95	1	no	—
74	D₁₉	—	5	1	no	—
75	C₃×D₅	—	19	1	no	—
76	C₃×D₅	—	361	1	no	—
77	C₃×D₅	—	361	1	no	—
78	C₃×D₅	—	361	1	no	—
79	C₁₉	—	6	3	no	—
80	C₁₉	C₃×D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
81	C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented
82	C₂×C₃²	—	1805	1	no	Hall
83	C₃×C₅	—	19	1	no	—
84	C₃×C₅	—	19	1	no	—
85	C₃×C₅	—	361	1	no	—
86	C₃×C₅	—	361	1	no	—
87	D₅	—	19	1	no	Hall
88	C₃²	—	361	1	no	Sylow
89	C₂×C₃	—	1805	1	no	—
90	C₂×C₃	—	1805	1	no	—
91	C₂×C₃	—	1805	1	no	—
92	C₂×C₃	—	95	1	no	—
93	C₅	C₁₉⋊C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
94	C₃	—	19	1	no	—
95	C₃	—	19	1	no	—
96	C₃	—	361	1	no	—
97	C₃	—	361	1	no	—
98	C₂	—	95	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₁₉⋊C₃²

C₂

yes

maximal, characteristic, complemented, Hall

C₁₉⋊C₃×D₉₅

C₃

yes

maximal, characteristic, complemented

C₅⋊#14524209

C₃

yes

maximal, characteristic, complemented

C₅⋊#14524208

C₃

yes

maximal, characteristic, complemented

C₁₉×C₅⋊(D₁₉⋊C₃)

C₃

yes

maximal, characteristic, complemented

C₁₉⋊C₃×D₁₉⋊C₃

—

maximal, Hall

C₅×#11762246

C₂×C₃

yes

characteristic, complemented

C₅×#11762245

C₂×C₃

yes

characteristic, complemented

C₅×C₁₉×C₁₉⋊C₃

C₂×C₃

yes

characteristic, complemented

C₅×C₁₉×C₁₉⋊C₃

C₂×C₃

yes

characteristic, complemented

C₁₉×D₉₅

C₃²

yes

characteristic, complemented, Hall

C₁₉⋊C₃²

D₅

yes

characteristic, complemented, Hall

D₁₉×C₁₉⋊C₃

—

#14524209

—

#14524208

—

C₁₉×D₁₉⋊C₃

—

C₅×C₁₉²

C₂×C₃²

yes

characteristic, complemented, Hall

C₃×C₅⋊(D₁₉⋊C₃)

—

maximal

C₃×D₅×C₁₉⋊C₃

—

maximal

#11762246

C₃×D₅

yes

characteristic, complemented

#11762245

C₃×D₅

yes

characteristic, complemented

C₁₉×C₁₉⋊C₃

C₃×D₅

yes

characteristic, complemented

C₁₉×C₁₉⋊C₃

C₃×D₅

yes

characteristic, complemented

C₃×C₅×C₁₉⋊C₃

—

C₃×C₅×C₁₉⋊C₃

—

C₁₉×D₁₉

—

Hall

C₃×D₉₅

—

C₃×D₅×C₁₉

—

C₅⋊(D₁₉⋊C₃)

—

C₅⋊(D₁₉⋊C₃)

—

C₅⋊(D₁₉⋊C₃)

C₁₉⋊C₃

yes

characteristic, direct product factor

D₅×C₁₉⋊C₃

—

D₅×C₁₉⋊C₃

—

D₅×C₁₉⋊C₃

—

C₁₉²

C₃²×D₅

yes

characteristic, complemented, Sylow

C₂×C₃×C₁₉⋊C₃

—

C₃×D₁₉⋊C₃

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

—

C₅×C₁₉⋊C₃

—

114

—

C₅×C₁₉⋊C₃

D₁₉⋊C₃

yes

characteristic, complemented

C₅×C₁₉⋊C₃

C₂×C₁₉⋊C₃

yes

characteristic, complemented

D₉₅

C₃×C₁₉⋊C₃

yes

characteristic, complemented

D₅×C₁₉

—

C₃×C₁₉⋊C₃

—

C₃×C₁₉⋊C₃

—

C₂×C₃×C₁₉

—

C₃×D₁₉

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

C₂×C₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

D₁₉⋊C₃

—

C₅×C₁₉

—

C₅×C₁₉

C₃×D₁₉⋊C₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×C₁₉⋊C₃

yes

characteristic, complemented

C₃²×D₅

—

361

Hall

C₃×C₁₉

—

C₃×C₁₉

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

114

—

C₁₉⋊C₃

D₅×C₁₉⋊C₃

yes

characteristic, complemented

C₁₉⋊C₃

C₅⋊(D₁₉⋊C₃)

yes

characteristic, direct product factor

C₃²×C₅

—

361

Hall

C₂×C₁₉

—

D₁₉

—

C₃×D₅

—

C₃×D₅

—

361

—

C₃×D₅

—

361

—

C₃×D₅

—

361

—

C₁₉

—

C₁₉

C₃×D₅×C₁₉⋊C₃

yes

characteristic, complemented

C₁₉

C₃×C₅⋊(D₁₉⋊C₃)

yes

characteristic, complemented

C₂×C₃²

—

1805

Hall

C₃×C₅

—

C₃×C₅

—

C₃×C₅

—

361

—

C₃×C₅

—

361

—

D₅

—

Hall

C₃²

—

361

Sylow

C₂×C₃

—

1805

—

C₂×C₃

—

1805

—

C₂×C₃

—

1805

—

C₂×C₃

—

C₅

C₁₉⋊C₃×D₁₉⋊C₃

yes

characteristic, complemented, Sylow

C₃

—

C₃

—

C₃

—

361

—

C₃

—

361

—

C₂

—

Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉²	C₂×C₃²
LCS	G ▷ C₅×C₁₉²
UCS	C₁

subgroup

G/H

center, Frattini, hypercenter

C₁

commutator, Fitting, socle, cosocle, hypocenter

C₅×C₁₉²

C₂×C₃²

LCS

G ▷ C₅×C₁₉²

UCS

C₁

N	H ≅ G/N	type
1. C₅×C₁₉⋊C₃²	C₂	semidirect
2. C₁₉⋊C₃×D₉₅	C₃	semidirect
3. C₅⋊#14524209	C₃	semidirect
4. C₅⋊#14524208	C₃	semidirect
5. C₁₉×C₅⋊(D₁₉⋊C₃)	C₃	semidirect
7. C₅×#11762246	C₂×C₃	semidirect
8. C₅×#11762245	C₂×C₃	semidirect
9. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
10. C₅×C₁₉×C₁₉⋊C₃	C₂×C₃	semidirect
11. C₁₉×D₉₅	C₃²	semidirect
12. C₁₉⋊C₃²	D₅	semidirect
17. C₅×C₁₉²	C₂×C₃²	semidirect
20. #11762246	C₃×D₅	semidirect
21. #11762245	C₃×D₅	semidirect
22. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
23. C₁₉×C₁₉⋊C₃	C₃×D₅	semidirect
31. C₅⋊(D₁₉⋊C₃)	C₁₉⋊C₃	direct (N × H)
35. C₁₉²	C₃²×D₅	semidirect
45. C₅×C₁₉⋊C₃	D₁₉⋊C₃	semidirect
46. C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	semidirect
47. D₉₅	C₃×C₁₉⋊C₃	semidirect
60. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
61. C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	semidirect
70. C₁₉⋊C₃	D₅×C₁₉⋊C₃	semidirect
71. C₁₉⋊C₃	C₅⋊(D₁₉⋊C₃)	direct (N × H)
80. C₁₉	C₃×D₅×C₁₉⋊C₃	semidirect
81. C₁₉	C₃×C₅⋊(D₁₉⋊C₃)	semidirect
93. C₅	C₁₉⋊C₃×D₁₉⋊C₃	semidirect

H ≅ G/N

type

1. C₅×C₁₉⋊C₃²

C₂

semidirect

2. C₁₉⋊C₃×D₉₅

C₃

semidirect

3. C₅⋊#14524209

C₃

semidirect

4. C₅⋊#14524208

C₃

semidirect

5. C₁₉×C₅⋊(D₁₉⋊C₃)

C₃

semidirect

7. C₅×#11762246

C₂×C₃

semidirect

8. C₅×#11762245

C₂×C₃

semidirect

9. C₅×C₁₉×C₁₉⋊C₃

C₂×C₃

semidirect

10. C₅×C₁₉×C₁₉⋊C₃

C₂×C₃

semidirect

11. C₁₉×D₉₅

C₃²

semidirect

12. C₁₉⋊C₃²

D₅

semidirect

17. C₅×C₁₉²

C₂×C₃²

semidirect

20. #11762246

C₃×D₅

semidirect

21. #11762245

C₃×D₅

semidirect

22. C₁₉×C₁₉⋊C₃

C₃×D₅

semidirect

23. C₁₉×C₁₉⋊C₃

C₃×D₅

semidirect

31. C₅⋊(D₁₉⋊C₃)

C₁₉⋊C₃

direct (N × H)

35. C₁₉²

C₃²×D₅

semidirect

45. C₅×C₁₉⋊C₃

D₁₉⋊C₃

semidirect

46. C₅×C₁₉⋊C₃

C₂×C₁₉⋊C₃

semidirect

47. D₉₅

C₃×C₁₉⋊C₃

semidirect

60. C₅×C₁₉

C₃×D₁₉⋊C₃

semidirect

61. C₅×C₁₉

C₂×C₃×C₁₉⋊C₃

semidirect

70. C₁₉⋊C₃

D₅×C₁₉⋊C₃

semidirect

71. C₁₉⋊C₃

C₅⋊(D₁₉⋊C₃)

direct (N × H)

80. C₁₉

C₃×D₅×C₁₉⋊C₃

semidirect

81. C₁₉

C₃×C₅⋊(D₁₉⋊C₃)

semidirect

93. C₅

C₁₉⋊C₃×D₁₉⋊C₃

semidirect

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

subgroup	index
C₅×C₁₉⋊C₃²	2
C₁₉⋊C₃×D₉₅	3
C₅⋊#14524209	3
C₅⋊#14524208	3
C₁₉×C₅⋊(D₁₉⋊C₃)	3
C₁₉⋊C₃×D₁₉⋊C₃	5
C₃×C₅⋊(D₁₉⋊C₃)	19
C₃×D₅×C₁₉⋊C₃	19

subgroup

index

C₅×C₁₉⋊C₃²

C₁₉⋊C₃×D₉₅

C₅⋊#14524209

C₅⋊#14524208

C₁₉×C₅⋊(D₁₉⋊C₃)

C₁₉⋊C₃×D₁₉⋊C₃

C₃×C₅⋊(D₁₉⋊C₃)

C₃×D₅×C₁₉⋊C₃

Subgroups — C₁₉⋊C₃×C₅⋊(D₁₉⋊C₃) #44570540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19⋊C3×C5⋊(D19⋊C3) #44570540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊C₃×C₅⋊(D₁₉⋊C₃) #44570540