Subgroups — C₂×D₃×C₄₇×C₁₉⋊C₃ #44565319

Order 32148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₄₇×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₉×C₄₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄₇×C₁₉⋊C₃	—	3	1	no	maximal
5	C₃×C₄₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₁₉×C₄₇	C₂×C₃	1	2	yes	complemented
7	C₂×C₄₇×C₁₉⋊C₃	—	2	1	no	—
8	C₂×C₄₇×C₁₉⋊C₃	—	3	2	no	—
9	C₂×C₄₇×C₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
10	C₂×C₃×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂²×C₁₉×C₄₇	—	3	1	no	Hall
12	C₃×C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₄₇×C₁₉⋊C₃	—	2	1	no	—
14	C₄₇×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₁₉×C₄₇	—	3	2	no	—
16	C₂×C₁₉×C₄₇	C₃×D₃	1	1	yes	characteristic, complemented
17	C₂×C₃×D₃×C₄₇	—	19	1	no	maximal, Hall
18	C₁₉×C₄₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃²×C₄₇	—	19	1	no	—
20	C₃×D₃×C₄₇	—	19	2	no	—
21	C₂×D₃×C₁₉⋊C₃	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₃×C₄₇	—	57	1	no	—
23	C₂×D₃×C₄₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
24	C₃²×C₄₇	—	19	1	no	Hall
25	C₂×C₃×C₁₉⋊C₃	C₂×C₄₇	1	1	yes	characteristic, complemented
26	D₃×C₁₉⋊C₃	C₂×C₄₇	1	2	yes	direct product factor
27	C₂×C₃×C₄₇	—	19	1	no	—
28	C₂×C₃×C₄₇	—	38	1	no	—
29	C₂×C₃×C₄₇	—	57	2	no	—
30	C₂×C₃×C₄₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	D₃×C₄₇	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
32	C₂×D₃×C₁₉	C₃×C₄₇	1	1	yes	characteristic, complemented
33	C₂²×C₁₉⋊C₃	—	3	1	no	—
34	C₂²×C₄₇	—	3	1	no	Hall
35	C₃×C₁₉⋊C₃	C₂²×C₄₇	1	1	yes	characteristic, complemented, Hall
36	C₃×C₄₇	—	19	1	no	—
37	C₃×C₄₇	—	38	1	no	—
38	C₃×C₄₇	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
39	C₂×C₃×C₁₉	C₂×C₃×C₄₇	1	1	yes	characteristic, complemented
40	D₃×C₁₉	C₂×C₃×C₄₇	1	2	yes	complemented
41	C₂×C₁₉⋊C₃	—	2	1	no	—
42	C₂×C₁₉⋊C₃	—	3	2	no	—
43	C₂×C₁₉⋊C₃	D₃×C₄₇	1	1	yes	characteristic, direct product factor
44	C₂×C₄₇	—	3	2	no	—
45	C₂×C₄₇	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
46	C₂²×C₁₉	—	3	1	no	Hall
47	C₃×C₁₉	C₂²×C₃×C₄₇	1	1	yes	characteristic, complemented
48	C₁₉⋊C₃	—	2	1	no	—
49	C₁₉⋊C₃	C₂×D₃×C₄₇	1	1	yes	characteristic, direct product factor
50	C₄₇	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₁₉	—	3	2	no	—
52	C₂×C₁₉	C₃×D₃×C₄₇	1	1	yes	characteristic, complemented
53	C₂×C₃×D₃	—	19	1	no	Hall
54	C₁₉	C₂×C₃×D₃×C₄₇	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₃²	—	19	1	no	—
56	C₃×D₃	—	19	2	no	—
57	C₂²×C₃	—	57	1	no	—
58	C₂×D₃	C₄₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
59	C₃²	—	19	1	no	Sylow
60	C₂×C₃	—	19	1	no	—
61	C₂×C₃	—	38	1	no	—
62	C₂×C₃	—	57	2	no	—
63	C₂×C₃	C₂×C₄₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₄₇×C₁₉⋊C₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	19	1	no	—
67	C₃	—	38	1	no	—
68	C₃	C₂²×C₄₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	D₃×C₄₇×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₃×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₉	C₂²×C₃×C₄₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₄₇	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄₇×C₁₉⋊C₃	C₂	semidirect
2. D₃×C₄₇×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₁₉×C₄₇	C₃	semidirect
5. C₃×C₄₇×C₁₉⋊C₃	C₂²	semidirect
6. D₃×C₁₉×C₄₇	C₂×C₃	semidirect
9. C₂×C₄₇×C₁₉⋊C₃	D₃	direct (N × H)
10. C₂×C₃×C₁₉×C₄₇	C₂×C₃	semidirect
12. C₃×C₁₉×C₄₇	C₂²×C₃	semidirect
14. C₄₇×C₁₉⋊C₃	C₂×D₃	direct (N × H)
16. C₂×C₁₉×C₄₇	C₃×D₃	semidirect
18. C₁₉×C₄₇	C₂×C₃×D₃	semidirect
21. C₂×D₃×C₁₉⋊C₃	C₄₇	direct (N × H)
23. C₂×D₃×C₄₇	C₁₉⋊C₃	direct (N × H)
25. C₂×C₃×C₁₉⋊C₃	C₂×C₄₇	semidirect
26. D₃×C₁₉⋊C₃	C₂×C₄₇	direct (N × H)
30. C₂×C₃×C₄₇	C₂×C₁₉⋊C₃	semidirect
31. D₃×C₄₇	C₂×C₁₉⋊C₃	direct (N × H)
32. C₂×D₃×C₁₉	C₃×C₄₇	semidirect
35. C₃×C₁₉⋊C₃	C₂²×C₄₇	semidirect
38. C₃×C₄₇	C₂²×C₁₉⋊C₃	semidirect
39. C₂×C₃×C₁₉	C₂×C₃×C₄₇	semidirect
40. D₃×C₁₉	C₂×C₃×C₄₇	semidirect
43. C₂×C₁₉⋊C₃	D₃×C₄₇	direct (N × H)
45. C₂×C₄₇	D₃×C₁₉⋊C₃	direct (N × H)
47. C₃×C₁₉	C₂²×C₃×C₄₇	semidirect
49. C₁₉⋊C₃	C₂×D₃×C₄₇	direct (N × H)
50. C₄₇	C₂×D₃×C₁₉⋊C₃	direct (N × H)
52. C₂×C₁₉	C₃×D₃×C₄₇	semidirect
54. C₁₉	C₂×C₃×D₃×C₄₇	semidirect
58. C₂×D₃	C₄₇×C₁₉⋊C₃	direct (N × H)
63. C₂×C₃	C₂×C₄₇×C₁₉⋊C₃	semidirect
64. D₃	C₂×C₄₇×C₁₉⋊C₃	direct (N × H)
68. C₃	C₂²×C₄₇×C₁₉⋊C₃	semidirect
70. C₂	D₃×C₄₇×C₁₉⋊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
C₂×C₃×C₄₇×C₁₉⋊C₃	2
D₃×C₄₇×C₁₉⋊C₃	2
C₂×D₃×C₁₉×C₄₇	3
C₂²×C₄₇×C₁₉⋊C₃	3
C₂×C₃×D₃×C₄₇	19
C₂×D₃×C₁₉⋊C₃	47

Subgroups — C2×D3×C47×C19⋊C3 #44565319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₄₇×C₁₉⋊C₃ #44565319