Subgroups — C₂×C₁₉×C₄₉⋊C₉ #30660488

Order 16758.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₄₉⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₁₉×C₄₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₉×C₄₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₉×C₇⋊C₉	—	7	1	no	maximal
5	C₂×C₁₉×C₄₉	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₉×C₇⋊C₉	—	7	1	no	—
7	C₁₉×C₄₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄₉⋊C₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
10	C₄₉⋊C₉	C₂×C₁₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₂×C₉×C₁₉	—	49	1	no	Hall
13	C₂×C₃×C₄₉	C₃×C₁₉	1	1	yes	characteristic
14	C₂×C₇×C₁₉	C₇⋊C₉	1	1	yes	characteristic
15	C₉×C₁₉	—	49	1	no	Hall
16	C₃×C₄₉	C₂×C₃×C₁₉	1	1	yes	characteristic
17	C₇×C₁₉	C₂×C₇⋊C₉	1	1	yes	characteristic
18	C₂×C₇⋊C₉	—	7	1	no	—
19	C₂×C₃×C₁₉	C₄₉⋊C₃	1	1	yes	characteristic
20	C₂×C₄₉	C₉×C₁₉	1	1	yes	characteristic, complemented, Hall
21	C₇⋊C₉	—	7	1	no	—
22	C₃×C₁₉	C₂×C₄₉⋊C₃	1	1	yes	characteristic
23	C₄₉	C₂×C₉×C₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₇	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
25	C₂×C₁₉	C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
27	C₁₉	C₂×C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	—	49	1	no	Hall
29	C₂×C₇	C₁₉×C₇⋊C₉	1	1	yes	characteristic
30	C₉	—	49	1	no	Sylow
31	C₇	C₂×C₁₉×C₇⋊C₉	1	1	yes	characteristic
32	C₂×C₃	C₁₉×C₄₉⋊C₃	1	1	yes	characteristic
33	C₃	C₂×C₁₉×C₄₉⋊C₃	1	1	yes	characteristic
34	C₂	C₁₉×C₄₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₄₉⋊C₃
commutator, hypocenter	C₄₉	C₂×C₉×C₁₉
Frattini	C₃×C₇	C₂×C₁₉×ΓL(1,𝔽₈)
Fitting	C₂×C₃×C₁₉×C₄₉	C₃
socle, prime radical	C₂×C₃×C₇×C₁₉	ΓL(1,𝔽₈)
cosocle	C₃×C₄₉	C₂×C₃×C₁₉
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₄₉⋊C₉	C₂	direct (N × H)
5. C₂×C₁₉×C₄₉	C₉	semidirect
7. C₁₉×C₄₉	C₂×C₉	semidirect
8. C₂×C₄₉⋊C₉	C₁₉	direct (N × H)
10. C₄₉⋊C₉	C₂×C₁₉	direct (N × H)
20. C₂×C₄₉	C₉×C₁₉	semidirect
23. C₄₉	C₂×C₉×C₁₉	semidirect
25. C₂×C₁₉	C₄₉⋊C₉	direct (N × H)
27. C₁₉	C₂×C₄₉⋊C₉	direct (N × H)
34. C₂	C₁₉×C₄₉⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×C₄₉⋊C₉	2
C₂×C₃×C₁₉×C₄₉	3
C₂×C₁₉×C₇⋊C₉	7
C₂×C₄₉⋊C₉	19

Subgroups — C2×C19×C49⋊C9 #30660488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×C₄₉⋊C₉ #30660488