Subgroups — C₃×C₄₉×C₂²⋊(C₁₉⋊C₃) #45691445

Order 33516.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₉×C₂²⋊(C₁₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄₉×C₁₉⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₉×C₄₉	—	3	1	no	—
5	C₃×C₇×C₂²⋊(C₁₉⋊C₃)	C₇	1	1	yes	maximal, characteristic
6	C₂²×C₁₉×C₄₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₄₉×C₁₉⋊C₃	—	4	3	no	—
8	C₃×C₁₉×C₄₉	A₄	1	1	yes	characteristic, complemented
9	C₂×C₁₉×C₄₉	—	3	1	no	—
10	C₃×A₄×C₄₉	—	19	1	no	maximal, Hall
11	C₂²×C₃×C₇×C₁₉	C₃×C₇	1	1	yes	characteristic
12	C₇×C₂²⋊(C₁₉⋊C₃)	C₃×C₇	1	3	yes	—
13	C₃×C₇×C₁₉⋊C₃	—	4	1	no	—
14	C₁₉×C₄₉	C₃×A₄	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₇×C₁₉	—	3	1	no	—
16	C₃×C₂²⋊(C₁₉⋊C₃)	C₄₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₃×C₄₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
18	A₄×C₄₉	—	19	3	no	—
19	C₂²×C₇×C₁₉	C₃²×C₇	1	1	yes	characteristic
20	C₃²×C₄₉	—	76	1	no	Hall
21	C₃×C₇×C₁₉	C₇×A₄	1	1	yes	characteristic
22	C₇×C₁₉⋊C₃	—	4	3	no	—
23	C₂×C₃×C₄₉	—	3	1	no	—
24	C₂×C₇×C₁₉	—	3	1	no	—
25	C₃×C₇×A₄	—	19	1	no	—
26	C₂²×C₃×C₁₉	C₃×C₄₉	1	1	yes	characteristic, complemented
27	C₂²⋊(C₁₉⋊C₃)	C₃×C₄₉	1	3	yes	direct product factor
28	C₂²×C₄₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₉⋊C₃	—	4	1	no	Hall
30	C₃×C₄₉	—	76	3	no	—
31	C₃×C₄₉	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
32	C₇×C₁₉	C₃×C₇×A₄	1	1	yes	characteristic
33	C₂×C₃×C₁₉	—	3	1	no	—
34	C₂×C₄₉	—	3	1	no	—
35	C₂²×C₃×C₇	C₇×C₁₉⋊C₃	1	1	yes	characteristic
36	C₇×A₄	—	19	3	no	—
37	C₂²×C₁₉	C₃²×C₄₉	1	1	yes	characteristic, complemented, Hall
38	C₃²×C₇	—	76	1	no	—
39	C₃×C₁₉	A₄×C₄₉	1	1	yes	characteristic, complemented
40	C₁₉⋊C₃	—	4	3	no	—
41	C₄₉	C₃×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃×C₇	—	3	1	no	—
43	C₂×C₁₉	—	3	1	no	—
44	C₃×A₄	—	19	1	no	Hall
45	C₂²×C₇	C₃×C₇×C₁₉⋊C₃	1	1	yes	characteristic
46	C₃×C₇	—	76	3	no	—
47	C₃×C₇	C₇×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
48	C₁₉	C₃×A₄×C₄₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₇	—	3	1	no	—
50	C₂²×C₃	C₄₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented
51	A₄	—	19	3	no	—
52	C₃²	—	76	1	no	Sylow
53	C₇	C₃×C₇×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
54	C₂×C₃	—	3	1	no	—
55	C₂²	C₃×C₄₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	76	3	no	—
57	C₃	C₄₉×C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₄₉	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₃²×C₄₉
Frattini	C₇	C₃×C₇×C₂²⋊(C₁₉⋊C₃)
Fitting	C₂²×C₃×C₁₉×C₄₉	C₃
socle	C₂²×C₃×C₇×C₁₉	C₃×C₇
prime radical	C₃×C₇×C₂²⋊(C₁₉⋊C₃)	C₇
cosocle	C₂²×C₇×C₁₉	C₃²×C₇
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₄₉×C₂²⋊(C₁₉⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₁₉×C₄₉	C₃	semidirect
6. C₂²×C₁₉×C₄₉	C₃²	semidirect
8. C₃×C₁₉×C₄₉	A₄	semidirect
14. C₁₉×C₄₉	C₃×A₄	semidirect
16. C₃×C₂²⋊(C₁₉⋊C₃)	C₄₉	direct (N × H)
17. C₂²×C₃×C₄₉	C₁₉⋊C₃	semidirect
26. C₂²×C₃×C₁₉	C₃×C₄₉	semidirect
27. C₂²⋊(C₁₉⋊C₃)	C₃×C₄₉	direct (N × H)
28. C₂²×C₄₉	C₃×C₁₉⋊C₃	semidirect
31. C₃×C₄₉	C₂²⋊(C₁₉⋊C₃)	direct (N × H)
37. C₂²×C₁₉	C₃²×C₄₉	semidirect
39. C₃×C₁₉	A₄×C₄₉	semidirect
41. C₄₉	C₃×C₂²⋊(C₁₉⋊C₃)	direct (N × H)
48. C₁₉	C₃×A₄×C₄₉	semidirect
50. C₂²×C₃	C₄₉×C₁₉⋊C₃	semidirect
55. C₂²	C₃×C₄₉×C₁₉⋊C₃	semidirect
57. C₃	C₄₉×C₂²⋊(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
C₄₉×C₂²⋊(C₁₉⋊C₃)	3
C₂²×C₃×C₁₉×C₄₉	3
C₃×C₄₉×C₁₉⋊C₃	4
C₃×C₇×C₂²⋊(C₁₉⋊C₃)	7
C₃×A₄×C₄₉	19

Subgroups — C3×C49×C22⋊(C19⋊C3) #45691445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₉×C₂²⋊(C₁₉⋊C₃) #45691445