Subgroups — C₃×D₂₉×D₁₉⋊C₃ #34090657

Order 19836.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉⋊C₃×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₉⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₉×D₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₉×D₂₉	C₃	1	1	yes	maximal, characteristic, complemented
5	D₂₉×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
6	C₃×C₂₉×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂₉⋊(D₁₉⋊C₃)	C₂×C₃	1	3	yes	complemented
8	C₂₉×D₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₁₉⋊C₃×D₂₉	C₂×C₃	1	3	yes	complemented
10	C₃×D₅₅₁	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×C₂₉×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₉×D₂₉	C₂×C₃	1	1	yes	characteristic, complemented
13	D₁₉×D₂₉	C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₉×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂₉×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
16	D₅₅₁	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₁₉×D₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₂₉×D₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₂×C₃²×D₂₉	—	19	1	no	maximal, Hall
20	C₂×C₃×D₁₉⋊C₃	—	29	1	no	maximal, Hall
21	C₁₉×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₂₉	—	19	1	no	—
23	C₃²×D₂₉	—	19	1	no	—
24	C₃²×D₂₉	—	19	1	no	—
25	C₂×C₃×D₂₉	—	19	3	no	—
26	C₂×C₃×D₂₉	—	57	1	no	—
27	C₂×C₃×C₁₉⋊C₃	—	29	1	no	—
28	C₃×D₁₉⋊C₃	—	29	1	no	—
29	C₃×D₁₉⋊C₃	D₂₉	1	1	yes	characteristic, direct product factor
30	C₃²×C₂₉	—	19	1	no	Hall
31	C₂×C₃×D₁₉	—	29	1	no	—
32	C₂×D₁₉⋊C₃	—	29	3	no	—
33	C₂×C₃×C₂₉	—	19	3	no	—
34	C₂×C₃×C₂₉	—	57	1	no	—
35	C₃×D₂₉	—	19	3	no	—
36	C₃×D₂₉	—	19	3	no	—
37	C₃×D₂₉	—	57	1	no	—
38	C₃×D₂₉	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×C₁₉⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
40	C₂×D₂₉	—	57	1	no	Hall
41	C₂×C₃×C₁₉	—	29	1	no	—
42	C₃×D₁₉	—	29	1	no	—
43	C₃×D₁₉	C₃×D₂₉	1	1	yes	characteristic, complemented
44	C₂×C₁₉⋊C₃	—	29	3	no	—
45	D₁₉⋊C₃	—	29	3	no	—
46	D₁₉⋊C₃	C₃×D₂₉	1	3	yes	direct product factor
47	C₃×C₂₉	—	19	3	no	—
48	C₃×C₂₉	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
49	C₂×D₁₉	—	29	1	no	Hall
50	C₂×C₂₉	—	57	1	no	—
51	D₂₉	—	57	1	no	—
52	D₂₉	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
53	C₃×C₁₉	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented
54	C₁₉⋊C₃	C₂×C₃×D₂₉	1	3	yes	complemented
55	C₂×C₁₉	—	29	1	no	—
56	D₁₉	—	29	1	no	—
57	D₁₉	C₃²×D₂₉	1	1	yes	characteristic, complemented
58	C₂²×C₃²	—	551	1	no	Hall
59	C₂₉	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₁₉	C₂×C₃²×D₂₉	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃²	—	19	1	no	—
62	C₂×C₃²	—	551	1	no	—
63	C₂×C₃²	—	551	1	no	—
64	C₂²×C₃	—	551	3	no	—
65	C₂²×C₃	—	1653	1	no	—
66	C₃²	—	19	1	no	Sylow
67	C₂×C₃	—	19	3	no	—
68	C₂×C₃	—	29	1	no	—
69	C₂×C₃	—	551	3	no	—
70	C₂×C₃	—	551	3	no	—
71	C₂×C₃	—	57	1	no	—
72	C₂×C₃	—	1653	1	no	—
73	C₂²	—	1653	1	no	Sylow
74	C₃	—	19	3	no	—
75	C₃	D₂₉×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
76	C₂	—	29	1	no	—
77	C₂	—	57	1	no	—
78	C₂	—	1653	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₂₉×D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉×C₂₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₂₉	C₂²×C₃
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₁₉⋊C₃×D₂₉	C₂	semidirect
2. C₃×C₂₉⋊(D₁₉⋊C₃)	C₂	semidirect
3. C₃×C₂₉×D₁₉⋊C₃	C₂	semidirect
4. C₃×D₁₉×D₂₉	C₃	semidirect
5. D₂₉×D₁₉⋊C₃	C₃	direct (N × H)
6. C₃×C₂₉×C₁₉⋊C₃	C₂²	semidirect
7. C₂₉⋊(D₁₉⋊C₃)	C₂×C₃	semidirect
8. C₂₉×D₁₉⋊C₃	C₂×C₃	semidirect
9. C₁₉⋊C₃×D₂₉	C₂×C₃	semidirect
10. C₃×D₅₅₁	C₂×C₃	semidirect
11. C₃×C₂₉×D₁₉	C₂×C₃	semidirect
12. C₃×C₁₉×D₂₉	C₂×C₃	semidirect
13. D₁₉×D₂₉	C₃²	semidirect
14. C₃×C₁₉×C₂₉	C₂²×C₃	semidirect
15. C₂₉×C₁₉⋊C₃	C₂²×C₃	semidirect
16. D₅₅₁	C₂×C₃²	semidirect
17. C₁₉×D₂₉	C₂×C₃²	semidirect
18. C₂₉×D₁₉	C₂×C₃²	semidirect
21. C₁₉×C₂₉	C₂²×C₃²	semidirect
29. C₃×D₁₉⋊C₃	D₂₉	direct (N × H)
38. C₃×D₂₉	D₁₉⋊C₃	direct (N × H)
39. C₃×C₁₉⋊C₃	C₂×D₂₉	semidirect
43. C₃×D₁₉	C₃×D₂₉	semidirect
46. D₁₉⋊C₃	C₃×D₂₉	direct (N × H)
48. C₃×C₂₉	C₂×D₁₉⋊C₃	semidirect
52. D₂₉	C₃×D₁₉⋊C₃	direct (N × H)
53. C₃×C₁₉	C₂×C₃×D₂₉	semidirect
54. C₁₉⋊C₃	C₂×C₃×D₂₉	semidirect
57. D₁₉	C₃²×D₂₉	semidirect
59. C₂₉	C₂×C₃×D₁₉⋊C₃	semidirect
60. C₁₉	C₂×C₃²×D₂₉	semidirect
75. C₃	D₂₉×D₁₉⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₉⋊C₃×D₂₉	2
C₃×C₂₉⋊(D₁₉⋊C₃)	2
C₃×C₂₉×D₁₉⋊C₃	2
C₃×D₁₉×D₂₉	3
D₂₉×D₁₉⋊C₃	3
C₂×C₃²×D₂₉	19
C₂×C₃×D₁₉⋊C₃	29

Subgroups — C3×D29×D19⋊C3 #34090657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₂₉×D₁₉⋊C₃ #34090657