Subgroups — C₃⋊D₃×C₁₉×C₄₉ #30660554

Order 16758.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₁₉×C₄₉	—	3	4	no	maximal
3	C₃×C₁₉×C₄₉	D₃	1	4	yes	complemented
4	C₇×C₃⋊D₃×C₁₉	C₇	1	1	yes	maximal, characteristic
5	C₂×C₁₉×C₄₉	—	9	1	no	Hall
6	C₃²×C₇×C₁₉	C₂×C₇	1	1	yes	characteristic
7	C₁₉×C₄₉	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
8	C₃⋊D₃×C₄₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	D₃×C₇×C₁₉	—	3	4	no	—
10	C₃²×C₄₉	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	D₃×C₇	1	4	yes	—
12	C₃⋊D₃×C₁₉	C₄₉	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₄₉	—	3	4	no	—
14	C₂×C₇×C₁₉	—	9	1	no	—
15	C₃²×C₁₉	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₉	D₃×C₁₉	1	4	yes	complemented
17	C₇×C₁₉	C₇×C₃⋊D₃	1	1	yes	characteristic
18	C₇×C₃⋊D₃	C₇×C₁₉	1	1	yes	characteristic
19	D₃×C₁₉	—	3	4	no	—
20	C₂×C₄₉	—	9	1	no	Hall
21	C₃²×C₇	C₂×C₇×C₁₉	1	1	yes	characteristic
22	C₃×C₁₉	D₃×C₄₉	1	4	yes	complemented
23	C₄₉	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
24	D₃×C₇	—	3	4	no	—
25	C₂×C₁₉	—	9	1	no	Hall
26	C₃×C₇	D₃×C₇×C₁₉	1	4	yes	—
27	C₁₉	C₃⋊D₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₃⋊D₃	C₁₉×C₄₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	9	1	no	—
30	C₃²	C₂×C₁₉×C₄₉	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×C₃⋊D₃×C₁₉	1	1	yes	characteristic
32	D₃	—	3	4	no	—
33	C₃	D₃×C₁₉×C₄₉	1	4	yes	complemented
34	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₄₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₁₉×C₄₉
Frattini	C₇	C₇×C₃⋊D₃×C₁₉
Fitting	C₃²×C₁₉×C₄₉	C₂
socle	C₃²×C₇×C₁₉	C₂×C₇
prime radical	C₇×C₃⋊D₃×C₁₉	C₇
cosocle	C₃²×C₇	C₂×C₇×C₁₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₉×C₄₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₉×C₄₉	C₂	semidirect
3. C₃×C₁₉×C₄₉	D₃	semidirect
7. C₁₉×C₄₉	C₃⋊D₃	direct (N × H)
8. C₃⋊D₃×C₄₉	C₁₉	direct (N × H)
10. C₃²×C₄₉	C₂×C₁₉	semidirect
12. C₃⋊D₃×C₁₉	C₄₉	direct (N × H)
15. C₃²×C₁₉	C₂×C₄₉	semidirect
16. C₃×C₄₉	D₃×C₁₉	semidirect
22. C₃×C₁₉	D₃×C₄₉	semidirect
23. C₄₉	C₃⋊D₃×C₁₉	direct (N × H)
27. C₁₉	C₃⋊D₃×C₄₉	direct (N × H)
28. C₃⋊D₃	C₁₉×C₄₉	direct (N × H)
30. C₃²	C₂×C₁₉×C₄₉	semidirect
33. C₃	D₃×C₁₉×C₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₉×C₄₉	2
D₃×C₁₉×C₄₉	3
C₇×C₃⋊D₃×C₁₉	7
C₃⋊D₃×C₄₉	19

Subgroups — C3⋊D3×C19×C49 #30660554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃×C₁₉×C₄₉ #30660554