Subgroups — C₅⋊((C₄₉⋊C₃)⋊D₁₃) #34062053

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	D₃₁₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	(C₄₉⋊C₃)⋊D₁₃	—	5	1	no	maximal, 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	D₅	1	1	yes	characteristic, complemented, Hall
7	C₅⋊(D₄₉⋊C₃)	—	13	1	no	maximal, Hall
8	C₅×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
9	D₆₃₇	—	5	1	no	Hall
10	D₄₅₅	—	7	1	no	—
11	C₅×C₄₉⋊C₃	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	ΓL(1,𝔽₈)⋊D₁₃	—	35	1	no	—
14	D₂₄₅	—	13	1	no	Hall
15	C₅×C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic
16	C₃×D₆₅	—	49	1	no	Hall
17	D₄₉⋊C₃	—	65	1	no	Hall
18	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
19	C₅×C₄₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₅⋊AGL(1,𝔽₇)	—	91	1	no	—
21	C₃×C₅×C₁₃	—	49	1	no	Hall
22	D₉₁	—	35	1	no	—
23	C₄₉⋊C₃	D₆₅	1	1	yes	characteristic, complemented, Hall
24	D₆₅	—	49	1	no	Hall
25	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
26	D₄₉	—	65	1	no	Hall
27	C₇×C₁₃	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₃×D₁₃	—	245	1	no	Hall
29	D₃₅	—	91	1	no	—
30	C₅×C₁₃	D₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
32	AGL(1,𝔽₇)	—	455	1	no	—
33	C₃×C₁₃	—	49	1	no	Hall
34	C₅×C₇	ΓL(1,𝔽₈)⋊D₁₃	1	1	yes	characteristic
35	C₃×D₅	—	637	1	no	Hall
36	D₁₃	—	245	1	no	Hall
37	ΓL(1,𝔽₈)	—	7	1	no	—
38	C₃×C₅	—	49	1	no	Hall
39	D₇	—	455	1	no	—
40	C₁₃	C₅⋊(D₄₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	637	1	no	Hall
42	C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	1	1	yes	characteristic
43	C₂×C₃	—	3185	1	no	Hall
44	C₅	(C₄₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	3185	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₁₃×C₄₉	C₂×C₃
Frattini	C₇	C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)
socle	C₅×C₇×C₁₃	AGL(1,𝔽₇)
LCS	G ▷ C₅×C₁₃×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₄₉⋊C₃	C₂	semidirect
2. D₃₁₈₅	C₃	semidirect
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. C₁₃×C₄₉⋊C₃	D₅	semidirect
11. C₅×C₄₉⋊C₃	D₁₃	semidirect
12. C₁₃×C₄₉	C₃×D₅	semidirect
19. C₅×C₄₉	C₃×D₁₃	semidirect
23. C₄₉⋊C₃	D₆₅	semidirect
30. C₅×C₁₃	D₄₉⋊C₃	semidirect
31. C₄₉	C₃×D₆₅	semidirect
40. C₁₃	C₅⋊(D₄₉⋊C₃)	semidirect
44. C₅	(C₄₉⋊C₃)⋊D₁₃	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
D₃₁₈₅	3
(C₄₉⋊C₃)⋊D₁₃	5
C₅⋊(ΓL(1,𝔽₈)⋊D₁₃)	7
C₅⋊(D₄₉⋊C₃)	13

Subgroups — C5⋊((C49⋊C3)⋊D13) #34062053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊((C₄₉⋊C₃)⋊D₁₃) #34062053