Subgroups — C₅×D₁₃×C₄₉⋊C₃ #34062029

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	C₅×D₁₃×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₃×C₄₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×ΓL(1,𝔽₈)×D₁₃	—	7	1	no	maximal
6	C₁₃×C₄₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₄₉⋊C₃	—	13	1	no	maximal, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
9	D₁₃×C₄₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₇×D₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₅×C₄₉⋊C₃	D₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃×C₄₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	ΓL(1,𝔽₈)×D₁₃	—	7	1	no	—
14	C₂×C₅×C₄₉	—	13	1	no	Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₃×C₅×D₁₃	—	49	1	no	Hall
17	C₂×C₄₉⋊C₃	—	13	1	no	Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
19	C₅×C₄₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×ΓL(1,𝔽₈)	—	91	1	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	C₇×D₁₃	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
23	C₄₉⋊C₃	C₅×D₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₅×D₁₃	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
25	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
26	C₂×C₄₉	—	13	1	no	Hall
27	C₇×C₁₃	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	C₃×D₁₃	—	49	1	no	Hall
29	C₂×C₅×C₇	—	13	1	no	—
30	C₅×C₁₃	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₃×C₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	91	1	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic
35	C₂×C₃×C₅	—	637	1	no	Hall
36	D₁₃	C₅×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
37	ΓL(1,𝔽₈)	—	7	1	no	—
38	C₃×C₅	—	49	1	no	Hall
39	C₂×C₇	—	13	1	no	—
40	C₁₃	C₂×C₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	13	1	no	Hall
42	C₇	C₅×ΓL(1,𝔽₈)×D₁₃	1	1	yes	characteristic
43	C₂×C₃	—	637	1	no	Hall
44	C₅	D₁₃×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₃×C₄₉⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₄₉	C₂×C₃×C₅
Frattini	C₇	C₅×ΓL(1,𝔽₈)×D₁₃
Fitting	C₅×C₁₃×C₄₉	C₂×C₃
socle	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)
LCS	G ▷ C₁₃×C₄₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₄₉⋊C₃	C₂	semidirect
2. C₅×D₁₃×C₄₉	C₃	semidirect
3. D₁₃×C₄₉⋊C₃	C₅	direct (N × H)
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. C₁₃×C₄₉⋊C₃	C₂×C₅	semidirect
9. D₁₃×C₄₉	C₃×C₅	semidirect
11. C₅×C₄₉⋊C₃	D₁₃	direct (N × H)
12. C₁₃×C₄₉	C₂×C₃×C₅	semidirect
19. C₅×C₄₉	C₃×D₁₃	semidirect
23. C₄₉⋊C₃	C₅×D₁₃	direct (N × H)
24. C₅×D₁₃	C₄₉⋊C₃	direct (N × H)
30. C₅×C₁₃	C₂×C₄₉⋊C₃	semidirect
31. C₄₉	C₃×C₅×D₁₃	semidirect
36. D₁₃	C₅×C₄₉⋊C₃	direct (N × H)
40. C₁₃	C₂×C₅×C₄₉⋊C₃	semidirect
44. C₅	D₁₃×C₄₉⋊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
C₅×C₁₃×C₄₉⋊C₃	2
C₅×D₁₃×C₄₉	3
D₁₃×C₄₉⋊C₃	5
C₅×ΓL(1,𝔽₈)×D₁₃	7
C₂×C₅×C₄₉⋊C₃	13

Subgroups — C5×D13×C49⋊C3 #34062029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₃×C₄₉⋊C₃ #34062029