Subgroups — C₁₃×C₅⋊(D₄₉⋊C₃) #34062049

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×D₄₉⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₅⋊AGL(1,𝔽₇)	—	7	1	no	maximal
6	C₁₃×C₄₉⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
7	C₅⋊(D₄₉⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
9	C₁₃×D₄₉	—	5	1	no	Hall
10	C₁₃×D₃₅	—	7	1	no	—
11	C₅×C₄₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	C₁₃×AGL(1,𝔽₇)	—	35	1	no	—
14	D₂₄₅	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
15	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₃×D₅×C₁₃	—	49	1	no	Hall
17	D₄₉⋊C₃	—	5	1	no	Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
19	C₅×C₄₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
20	C₅⋊AGL(1,𝔽₇)	—	7	1	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₁₃×D₇	—	35	1	no	—
23	C₄₉⋊C₃	D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
24	D₅×C₁₃	—	49	1	no	Hall
25	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
26	D₄₉	—	5	1	no	Hall
27	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₂×C₃×C₁₃	—	245	1	no	Hall
29	D₃₅	—	7	1	no	—
30	C₅×C₁₃	D₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₃×D₅×C₁₃	1	1	yes	characteristic, complemented, Sylow
32	AGL(1,𝔽₇)	—	35	1	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic
35	C₃×D₅	—	49	1	no	Hall
36	C₂×C₁₃	—	245	1	no	Hall
37	ΓL(1,𝔽₈)	—	7	1	no	—
38	C₃×C₅	—	49	1	no	Hall
39	D₇	—	35	1	no	—
40	C₁₃	C₅⋊(D₄₉⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	—	49	1	no	Hall
42	C₇	C₁₃×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic
43	C₂×C₃	—	245	1	no	Hall
44	C₅	C₁₃×D₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	C₅⋊(D₄₉⋊C₃)
commutator, cosocle, hypocenter	C₅×C₄₉	C₂×C₃×C₁₃
Frattini	C₇	C₁₃×C₅⋊AGL(1,𝔽₇)
Fitting	C₅×C₁₃×C₄₉	C₂×C₃
socle	C₅×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₅×C₄₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₄₉⋊C₃	C₂	semidirect
2. C₁₃×D₂₄₅	C₃	semidirect
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. C₁₃×C₄₉⋊C₃	D₅	semidirect
7. C₅⋊(D₄₉⋊C₃)	C₁₃	direct (N × H)
11. C₅×C₄₉⋊C₃	C₂×C₁₃	semidirect
12. C₁₃×C₄₉	C₃×D₅	semidirect
14. D₂₄₅	C₃×C₁₃	semidirect
19. C₅×C₄₉	C₂×C₃×C₁₃	semidirect
23. C₄₉⋊C₃	D₅×C₁₃	semidirect
30. C₅×C₁₃	D₄₉⋊C₃	semidirect
31. C₄₉	C₃×D₅×C₁₃	semidirect
40. C₁₃	C₅⋊(D₄₉⋊C₃)	direct (N × H)
44. C₅	C₁₃×D₄₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×C₄₉⋊C₃	2
C₁₃×D₂₄₅	3
C₁₃×D₄₉⋊C₃	5
C₁₃×C₅⋊AGL(1,𝔽₇)	7
C₅⋊(D₄₉⋊C₃)	13

Subgroups — C13×C5⋊(D49⋊C3) #34062049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₅⋊(D₄₉⋊C₃) #34062049