Subgroups — C₅⋊#16838413 #34062046

Order 19110.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14274254	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₉×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16838413	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊#10587716	—	7	1	no	maximal
6	#14274254	D₅	1	1	yes	characteristic, complemented, Hall
7	D₅×C₄₉⋊C₃	—	13	1	no	maximal, Hall
8	C₅×#63270	—	7	1	no	—
9	D₁₃×C₄₉	—	5	1	no	Hall
10	C₇×D₆₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₅×C₄₉⋊C₃	—	13	1	no	Hall
12	C₁₃×C₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	#10587716	—	35	1	no	—
14	D₅×C₄₉	—	39	1	no	Hall
15	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₅⋊(D₁₃⋊C₃)	—	49	1	no	Hall
17	C₂×C₄₉⋊C₃	—	65	1	no	Hall
18	#63270	—	7	1	no	—
19	C₅×C₄₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	D₅×ΓL(1,𝔽₈)	—	91	1	no	—
21	C₅×C₁₃⋊C₃	—	49	1	no	Hall
22	C₇×D₁₃	—	5	1	no	—
23	C₄₉⋊C₃	—	13	1	no	Hall
24	D₆₅	C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
25	C₅×ΓL(1,𝔽₈)	—	91	1	no	—
26	C₂×C₄₉	—	195	1	no	Hall
27	C₇×C₁₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
28	D₁₃⋊C₃	—	245	1	no	Hall
29	C₇×D₅	—	39	1	no	—
30	C₅×C₁₃	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	455	1	no	—
33	C₁₃⋊C₃	—	49	1	no	Hall
34	C₅×C₇	#10587716	1	1	yes	characteristic
35	C₃×D₅	—	637	1	no	Hall
36	D₁₃	—	5	1	no	Hall
37	ΓL(1,𝔽₈)	—	91	1	no	—
38	C₃×C₅	—	637	1	no	Hall
39	C₂×C₇	—	195	1	no	—
40	C₁₃	D₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	39	1	no	Hall
42	C₇	C₅⋊#10587716	1	1	yes	characteristic
43	C₂×C₃	—	3185	1	no	Hall
44	C₅	#16838413	1	1	yes	characteristic, complemented, Sylow
45	C₃	—	637	1	no	Sylow
46	C₂	—	195	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₁₃×C₄₉	C₂×C₃
Frattini	C₇	C₅⋊#10587716
socle	C₅×C₇×C₁₃	C₂×ΓL(1,𝔽₈)
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×#14274254	C₂	semidirect
2. C₄₉×D₆₅	C₃	semidirect
4. C₅×C₁₃×C₄₉	C₂×C₃	semidirect
6. #14274254	D₅	semidirect
12. C₁₃×C₄₉	C₃×D₅	semidirect
19. C₅×C₄₉	D₁₃⋊C₃	semidirect
24. D₆₅	C₄₉⋊C₃	semidirect
30. C₅×C₁₃	C₂×C₄₉⋊C₃	semidirect
31. C₄₉	C₅⋊(D₁₃⋊C₃)	semidirect
40. C₁₃	D₅×C₄₉⋊C₃	semidirect
44. C₅	#16838413	semidirect

Maximal subgroups

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

subgroup	index
C₅×#14274254	2
C₄₉×D₆₅	3
#16838413	5
C₅⋊#10587716	7
D₅×C₄₉⋊C₃	13

Subgroups — C5⋊#16838413 #34062046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊#16838413 #34062046