Subgroups — C₅×#19154245 #44415913

Order 29190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#15668589	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#19154245	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×D₁₃₉⋊C₃	—	7	1	no	maximal, Hall
6	#15668589	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₃₉⋊C₃	—	7	1	no	Hall
8	C₇×D₁₃₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₅×D₁₃₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₃₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	D₁₃₉⋊C₃	—	7	1	no	Hall
12	C₅×C₁₃₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₁₃₉⋊C₃	—	7	1	no	Hall
14	D₁₃₉	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×ΓL(1,𝔽₈)	—	139	1	no	maximal, Hall
16	C₁₃₉	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
17	C₅×ΓL(1,𝔽₈)	—	139	1	no	Hall
18	C₂×C₅×C₇	—	139	1	no	Hall
19	C₂×ΓL(1,𝔽₈)	—	139	1	no	Hall
20	C₅×C₇	D₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅	—	973	1	no	Hall
22	ΓL(1,𝔽₈)	—	139	1	no	Hall
23	C₃×C₅	—	973	1	no	Hall
24	C₂×C₇	—	139	1	no	Hall
25	C₂×C₅	—	139	1	no	Hall
26	C₇	C₅×D₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	973	1	no	Hall
28	C₅	#19154245	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	973	1	no	Sylow
30	C₂	—	139	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#19154245
commutator, cosocle, hypocenter	C₇×C₁₃₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃₉	C₂×C₃
LCS	G ▷ C₇×C₁₃₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#15668589	C₂	semidirect
2. C₅×C₇×D₁₃₉	C₃	semidirect
3. #19154245	C₅	direct (N × H)
4. C₅×C₇×C₁₃₉	C₂×C₃	semidirect
6. #15668589	C₂×C₅	semidirect
8. C₇×D₁₃₉	C₃×C₅	semidirect
9. C₅×D₁₃₉	ΓL(1,𝔽₈)	semidirect
10. C₇×C₁₃₉	C₂×C₃×C₅	semidirect
12. C₅×C₁₃₉	C₂×ΓL(1,𝔽₈)	semidirect
14. D₁₃₉	C₅×ΓL(1,𝔽₈)	semidirect
16. C₁₃₉	C₂×C₅×ΓL(1,𝔽₈)	semidirect
20. C₅×C₇	D₁₃₉⋊C₃	semidirect
26. C₇	C₅×D₁₃₉⋊C₃	semidirect
28. C₅	#19154245	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×#15668589	2
C₅×C₇×D₁₃₉	3
#19154245	5
C₅×D₁₃₉⋊C₃	7
C₂×C₅×ΓL(1,𝔽₈)	139

Subgroups — C5×#19154245 #44415913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19154245 #44415913