Group #44570513 — subgroups

Subgroups — C₅×C₁₉⋊C₃×D₁₉⋊C₃ #44570513

Order 32490.

108 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 38 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	C₅×D₁₉×C₁₉⋊C₃	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	C₅×C₁₉×D₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₉⋊C₃×D₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, 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	C₅×C₁₉×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₁₉⋊C₃²	C₂×C₅	1	1	yes	characteristic, complemented, Hall
13	D₁₉×C₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
14	#14524209	C₃×C₅	1	1	yes	characteristic, complemented
15	#14524208	C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₉×D₁₉⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
17	C₅×C₁₉²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅×C₁₉⋊C₃	—	19	1	no	maximal
19	C₃×C₅×D₁₉⋊C₃	—	19	1	no	maximal
20	#11762246	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	#11762245	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
23	C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
25	C₃×C₅×C₁₉⋊C₃	—	19	1	no	—
26	C₁₉×D₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₅×C₁₉	—	19	1	no	—
28	C₃×C₅×D₁₉	—	19	1	no	—
29	C₂×C₅×C₁₉⋊C₃	—	19	1	no	—
30	C₂×C₅×C₁₉⋊C₃	—	19	1	no	—
31	C₂×C₅×C₁₉⋊C₃	—	19	1	no	—
32	C₅×D₁₉⋊C₃	—	19	1	no	—
33	C₅×D₁₉⋊C₃	—	19	1	no	—
34	C₅×D₁₉⋊C₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
35	C₁₉²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₉⋊C₃	—	19	1	no	—
37	C₃×D₁₉⋊C₃	—	19	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, direct product factor
46	C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₂×C₅×C₁₉	—	19	1	no	—
48	C₅×D₁₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₃×C₁₉⋊C₃	—	19	1	no	—
50	C₃×C₁₉⋊C₃	—	19	1	no	—
51	C₂×C₃×C₁₉	—	19	1	no	—
52	C₃×D₁₉	—	19	1	no	—
53	C₂×C₁₉⋊C₃	—	19	1	no	—
54	C₂×C₁₉⋊C₃	—	19	1	no	—
55	C₂×C₁₉⋊C₃	—	19	1	no	—
56	D₁₉⋊C₃	—	19	1	no	—
57	D₁₉⋊C₃	—	19	1	no	—
58	D₁₉⋊C₃	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
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	C₂×C₃²×C₅	—	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	C₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
71	C₁₉⋊C₃	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
72	C₃²×C₅	—	361	1	no	Hall
73	C₂×C₁₉	—	19	1	no	—
74	D₁₉	C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
75	C₂×C₃×C₅	—	19	1	no	—
76	C₂×C₃×C₅	—	361	1	no	—
77	C₂×C₃×C₅	—	361	1	no	—
78	C₂×C₃×C₅	—	361	1	no	—
79	C₁₉	—	6	3	no	—
80	C₁₉	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic, complemented
81	C₁₉	C₂×C₃×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
82	C₂×C₃²	—	361	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	C₂×C₅	—	19	1	no	Hall
88	C₃²	—	361	1	no	Sylow
89	C₂×C₃	—	19	1	no	—
90	C₂×C₃	—	361	1	no	—
91	C₂×C₃	—	361	1	no	—
92	C₂×C₃	—	361	1	no	—
93	C₅	C₁₉⋊C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
94	C₃	—	19	1	no	—
95	C₃	—	19	1	no	—
96	C₃	—	361	1	no	—
97	C₃	—	361	1	no	—
98	C₂	—	19	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₁₉⋊C₃²

C₂

yes

maximal, characteristic, complemented, Hall

C₅×D₁₉×C₁₉⋊C₃

C₃

yes

maximal, characteristic, complemented

C₅×#14524209

C₃

yes

maximal, characteristic, complemented

C₅×#14524208

C₃

yes

maximal, characteristic, complemented

C₅×C₁₉×D₁₉⋊C₃

C₃

yes

maximal, characteristic, complemented

C₁₉⋊C₃×D₁₉⋊C₃

C₅

yes

maximal, characteristic, direct product factor, 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

C₅×C₁₉×D₁₉

C₃²

yes

characteristic, complemented, Hall

C₁₉⋊C₃²

C₂×C₅

yes

characteristic, complemented, Hall

D₁₉×C₁₉⋊C₃

C₃×C₅

yes

characteristic, complemented

#14524209

C₃×C₅

yes

characteristic, complemented

#14524208

C₃×C₅

yes

characteristic, complemented

C₁₉×D₁₉⋊C₃

C₃×C₅

yes

characteristic, complemented

C₅×C₁₉²

C₂×C₃²

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₉⋊C₃

—

maximal

C₃×C₅×D₁₉⋊C₃

—

maximal

#11762246

C₂×C₃×C₅

yes

characteristic, complemented

#11762245

C₂×C₃×C₅

yes

characteristic, complemented

C₁₉×C₁₉⋊C₃

C₂×C₃×C₅

yes

characteristic, complemented

C₁₉×C₁₉⋊C₃

C₂×C₃×C₅

yes

characteristic, complemented

C₃×C₅×C₁₉⋊C₃

—

C₃×C₅×C₁₉⋊C₃

—

C₁₉×D₁₉

C₃²×C₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅×C₁₉

—

C₃×C₅×D₁₉

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₂×C₅×C₁₉⋊C₃

—

C₅×D₁₉⋊C₃

—

C₅×D₁₉⋊C₃

—

C₅×D₁₉⋊C₃

C₁₉⋊C₃

yes

characteristic, direct product factor

C₁₉²

C₂×C₃²×C₅

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, direct product factor

C₅×C₁₉⋊C₃

C₂×C₁₉⋊C₃

yes

characteristic, complemented

C₂×C₅×C₁₉

—

C₅×D₁₉

C₃×C₁₉⋊C₃

yes

characteristic, complemented

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⋊C₃

yes

characteristic, direct product factor

C₅×C₁₉

—

C₅×C₁₉

C₃×D₁₉⋊C₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃×C₁₉⋊C₃

yes

characteristic, complemented

C₂×C₃²×C₅

—

361

Hall

C₃×C₁₉

—

C₃×C₁₉

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

C₁₉⋊C₃

—

114

—

C₁₉⋊C₃

C₅×D₁₉⋊C₃

yes

characteristic, direct product factor

C₁₉⋊C₃

C₂×C₅×C₁₉⋊C₃

yes

characteristic, complemented

C₃²×C₅

—

361

Hall

C₂×C₁₉

—

D₁₉

C₃×C₅×C₁₉⋊C₃

yes

characteristic, complemented

C₂×C₃×C₅

—

C₂×C₃×C₅

—

361

—

C₂×C₃×C₅

—

361

—

C₂×C₃×C₅

—

361

—

C₁₉

—

C₁₉

C₃×C₅×D₁₉⋊C₃

yes

characteristic, complemented

C₁₉

C₂×C₃×C₅×C₁₉⋊C₃

yes

characteristic, complemented

C₂×C₃²

—

361

Hall

C₃×C₅

—

C₃×C₅

—

C₃×C₅

—

361

—

C₃×C₅

—

361

—

C₂×C₅

—

Hall

C₃²

—

361

Sylow

C₂×C₃

—

C₂×C₃

—

361

—

C₂×C₃

—

361

—

C₂×C₃

—

361

—

C₅

C₁₉⋊C₃×D₁₉⋊C₃

yes

characteristic, direct product factor, Sylow

C₃

—

C₃

—

C₃

—

361

—

C₃

—

361

—

C₂

—

Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₉⋊C₃×D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₉²	C₂×C₃²
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

C₁₉⋊C₃×D₁₉⋊C₃

commutator, cosocle, hypocenter

C₁₉²

C₂×C₃²×C₅

Frattini

C₁

Fitting, socle

C₅×C₁₉²

C₂×C₃²

LCS

G ▷ C₁₉²

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₅×C₁₉⋊C₃²	C₂	semidirect
2. C₅×D₁₉×C₁₉⋊C₃	C₃	semidirect
3. C₅×#14524209	C₃	semidirect
4. C₅×#14524208	C₃	semidirect
5. C₅×C₁₉×D₁₉⋊C₃	C₃	semidirect
6. C₁₉⋊C₃×D₁₉⋊C₃	C₅	direct (N × H)
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. C₅×C₁₉×D₁₉	C₃²	semidirect
12. C₁₉⋊C₃²	C₂×C₅	semidirect
13. D₁₉×C₁₉⋊C₃	C₃×C₅	semidirect
14. #14524209	C₃×C₅	semidirect
15. #14524208	C₃×C₅	semidirect
16. C₁₉×D₁₉⋊C₃	C₃×C₅	semidirect
17. C₅×C₁₉²	C₂×C₃²	semidirect
20. #11762246	C₂×C₃×C₅	semidirect
21. #11762245	C₂×C₃×C₅	semidirect
22. C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
23. C₁₉×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
26. C₁₉×D₁₉	C₃²×C₅	semidirect
34. C₅×D₁₉⋊C₃	C₁₉⋊C₃	direct (N × H)
35. C₁₉²	C₂×C₃²×C₅	semidirect
45. C₅×C₁₉⋊C₃	D₁₉⋊C₃	direct (N × H)
46. C₅×C₁₉⋊C₃	C₂×C₁₉⋊C₃	semidirect
48. C₅×D₁₉	C₃×C₁₉⋊C₃	semidirect
58. D₁₉⋊C₃	C₅×C₁₉⋊C₃	direct (N × H)
60. C₅×C₁₉	C₃×D₁₉⋊C₃	semidirect
61. C₅×C₁₉	C₂×C₃×C₁₉⋊C₃	semidirect
70. C₁₉⋊C₃	C₅×D₁₉⋊C₃	direct (N × H)
71. C₁₉⋊C₃	C₂×C₅×C₁₉⋊C₃	semidirect
74. D₁₉	C₃×C₅×C₁₉⋊C₃	semidirect
80. C₁₉	C₃×C₅×D₁₉⋊C₃	semidirect
81. C₁₉	C₂×C₃×C₅×C₁₉⋊C₃	semidirect
93. C₅	C₁₉⋊C₃×D₁₉⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₅×C₁₉⋊C₃²

C₂

semidirect

2. C₅×D₁₉×C₁₉⋊C₃

C₃

semidirect

3. C₅×#14524209

C₃

semidirect

4. C₅×#14524208

C₃

semidirect

5. C₅×C₁₉×D₁₉⋊C₃

C₃

semidirect

6. C₁₉⋊C₃×D₁₉⋊C₃

C₅

direct (N × H)

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. C₅×C₁₉×D₁₉

C₃²

semidirect

12. C₁₉⋊C₃²

C₂×C₅

semidirect

13. D₁₉×C₁₉⋊C₃

C₃×C₅

semidirect

14. #14524209

C₃×C₅

semidirect

15. #14524208

C₃×C₅

semidirect

16. C₁₉×D₁₉⋊C₃

C₃×C₅

semidirect

17. C₅×C₁₉²

C₂×C₃²

semidirect

20. #11762246

C₂×C₃×C₅

semidirect

21. #11762245

C₂×C₃×C₅

semidirect

22. C₁₉×C₁₉⋊C₃

C₂×C₃×C₅

semidirect

23. C₁₉×C₁₉⋊C₃

C₂×C₃×C₅

semidirect

26. C₁₉×D₁₉

C₃²×C₅

semidirect

34. C₅×D₁₉⋊C₃

C₁₉⋊C₃

direct (N × H)

35. C₁₉²

C₂×C₃²×C₅

semidirect

45. C₅×C₁₉⋊C₃

D₁₉⋊C₃

direct (N × H)

46. C₅×C₁₉⋊C₃

C₂×C₁₉⋊C₃

semidirect

48. C₅×D₁₉

C₃×C₁₉⋊C₃

semidirect

58. D₁₉⋊C₃

C₅×C₁₉⋊C₃

direct (N × H)

60. C₅×C₁₉

C₃×D₁₉⋊C₃

semidirect

61. C₅×C₁₉

C₂×C₃×C₁₉⋊C₃

semidirect

70. C₁₉⋊C₃

C₅×D₁₉⋊C₃

direct (N × H)

71. C₁₉⋊C₃

C₂×C₅×C₁₉⋊C₃

semidirect

74. D₁₉

C₃×C₅×C₁₉⋊C₃

semidirect

80. C₁₉

C₃×C₅×D₁₉⋊C₃

semidirect

81. C₁₉

C₂×C₃×C₅×C₁₉⋊C₃

semidirect

93. C₅

C₁₉⋊C₃×D₁₉⋊C₃

direct (N × H)

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

subgroup	index
C₅×C₁₉⋊C₃²	2
C₅×D₁₉×C₁₉⋊C₃	3
C₅×#14524209	3
C₅×#14524208	3
C₅×C₁₉×D₁₉⋊C₃	3
C₁₉⋊C₃×D₁₉⋊C₃	5
C₂×C₃×C₅×C₁₉⋊C₃	19
C₃×C₅×D₁₉⋊C₃	19

subgroup

index

C₅×C₁₉⋊C₃²

C₅×D₁₉×C₁₉⋊C₃

C₅×#14524209

C₅×#14524208

C₅×C₁₉×D₁₉⋊C₃

C₁₉⋊C₃×D₁₉⋊C₃

C₂×C₃×C₅×C₁₉⋊C₃

C₃×C₅×D₁₉⋊C₃

Subgroups — C₅×C₁₉⋊C₃×D₁₉⋊C₃ #44570513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×C19⋊C3×D19⋊C3 #44570513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉⋊C₃×D₁₉⋊C₃ #44570513