Subgroups — C₅×D₂₁×C₁₉⋊C₃ #26046196

Order 11970.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇×C₁₉⋊C₃	—	3	1	no	maximal
3	C₅×C₁₉×D₂₁	C₃	1	1	yes	maximal, characteristic, complemented
4	D₂₁×C₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×C₇×C₁₉⋊C₃	—	2	1	no	—
7	C₅×C₇×C₁₉⋊C₃	D₃	1	1	yes	characteristic, complemented
8	C₅×D₃×C₁₉⋊C₃	—	7	1	no	maximal, Hall
9	C₅×D₇×C₁₉	—	3	1	no	Hall
10	C₃×C₇×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
12	C₁₉×D₂₁	C₃×C₅	1	1	yes	characteristic, complemented
13	D₇×C₁₉⋊C₃	—	3	1	no	—
14	C₅×C₇×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×D₂₁	—	19	1	no	maximal, Hall
16	C₅×D₃×C₁₉	—	7	1	no	—
17	C₂×C₅×C₁₉⋊C₃	—	21	1	no	—
18	C₃×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₇×C₁₉⋊C₃	—	2	1	no	—
20	C₇×C₁₉⋊C₃	C₅×D₃	1	1	yes	characteristic, complemented
21	D₃×C₁₉⋊C₃	—	7	1	no	Hall
22	C₃²×C₅×C₇	—	19	1	no	Hall
23	C₃×C₅×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
24	C₅×C₁₉⋊C₃	—	2	1	no	—
25	C₅×C₁₉⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
26	D₇×C₁₉	—	3	1	no	Hall
27	C₅×D₂₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
28	C₃×C₅×D₇	—	57	1	no	—
29	C₂×C₅×C₁₉	—	21	1	no	Hall
30	C₃×C₁₉⋊C₃	C₅×D₇	1	1	yes	characteristic, complemented, Hall
31	C₇×C₁₉	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Hall
32	C₃×D₂₁	—	19	1	no	Hall
33	D₃×C₁₉	—	7	1	no	—
34	C₂×C₁₉⋊C₃	—	21	1	no	—
35	C₃×C₅×C₇	—	19	1	no	—
36	C₃×C₅×C₇	—	38	1	no	—
37	C₃×C₅×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
38	C₅×C₁₉	C₃×D₂₁	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×D₃	—	133	1	no	Hall
40	C₅×D₇	—	3	1	no	Hall
41	C₃²×C₇	—	19	1	no	Hall
42	C₃×C₁₉	C₃×C₅×D₇	1	1	yes	characteristic, complemented
43	C₁₉⋊C₃	—	2	1	no	—
44	C₁₉⋊C₃	C₅×D₂₁	1	1	yes	characteristic, direct product factor
45	C₃²×C₅	—	19	1	no	Hall
46	D₂₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
47	C₃×D₇	—	57	1	no	—
48	C₂×C₁₉	—	21	1	no	Hall
49	C₅×C₇	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₅	—	399	1	no	—
51	C₅×D₃	—	7	1	no	—
52	C₃×C₇	—	19	1	no	—
53	C₃×C₇	—	38	1	no	—
54	C₃×C₇	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
55	C₁₉	C₃×C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
56	C₃×D₃	—	133	1	no	Hall
57	C₃×C₅	—	19	1	no	—
58	C₃×C₅	—	38	1	no	—
59	C₃×C₅	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
60	D₇	—	3	1	no	Hall
61	C₂×C₅	—	21	1	no	Hall
62	C₃²	—	19	1	no	Sylow
63	C₇	C₅×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	399	1	no	—
65	D₃	—	7	1	no	—
66	C₅	D₂₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	19	1	no	—
68	C₃	—	38	1	no	—
69	C₃	C₅×D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
70	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₁×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₉⋊C₃	C₂	semidirect
3. C₅×C₁₉×D₂₁	C₃	semidirect
4. D₂₁×C₁₉⋊C₃	C₅	direct (N × H)
5. C₃×C₅×C₇×C₁₉	C₂×C₃	semidirect
7. C₅×C₇×C₁₉⋊C₃	D₃	semidirect
10. C₃×C₇×C₁₉⋊C₃	C₂×C₅	semidirect
11. C₃×C₅×C₁₉⋊C₃	D₇	semidirect
12. C₁₉×D₂₁	C₃×C₅	semidirect
14. C₅×C₇×C₁₉	C₃×D₃	semidirect
18. C₃×C₇×C₁₉	C₂×C₃×C₅	semidirect
20. C₇×C₁₉⋊C₃	C₅×D₃	semidirect
23. C₃×C₅×C₁₉	C₃×D₇	semidirect
25. C₅×C₁₉⋊C₃	D₂₁	direct (N × H)
27. C₅×D₂₁	C₁₉⋊C₃	direct (N × H)
30. C₃×C₁₉⋊C₃	C₅×D₇	semidirect
31. C₇×C₁₉	C₃×C₅×D₃	semidirect
37. C₃×C₅×C₇	C₂×C₁₉⋊C₃	semidirect
38. C₅×C₁₉	C₃×D₂₁	semidirect
42. C₃×C₁₉	C₃×C₅×D₇	semidirect
44. C₁₉⋊C₃	C₅×D₂₁	direct (N × H)
46. D₂₁	C₅×C₁₉⋊C₃	direct (N × H)
49. C₅×C₇	D₃×C₁₉⋊C₃	semidirect
54. C₃×C₇	C₂×C₅×C₁₉⋊C₃	semidirect
55. C₁₉	C₃×C₅×D₂₁	semidirect
59. C₃×C₅	D₇×C₁₉⋊C₃	semidirect
63. C₇	C₅×D₃×C₁₉⋊C₃	semidirect
66. C₅	D₂₁×C₁₉⋊C₃	direct (N × H)
69. C₃	C₅×D₇×C₁₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₉⋊C₃	2
C₅×D₇×C₁₉⋊C₃	3
C₅×C₁₉×D₂₁	3
D₂₁×C₁₉⋊C₃	5
C₅×D₃×C₁₉⋊C₃	7
C₃×C₅×D₂₁	19

Subgroups — C5×D21×C19⋊C3 #26046196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₂₁×C₁₉⋊C₃ #26046196