Subgroups — C₁₃×AGL(1,𝔽₇)×C₅₉ #44567280

Order 32214.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×ΓL(1,𝔽₈)×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₇×C₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₅₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₅₉	—	7	1	no	maximal, Hall
5	AGL(1,𝔽₇)×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₁₃×C₅₉	—	7	1	no	Hall
7	C₂×C₁₃×C₅₉	—	7	1	no	Hall
8	ΓL(1,𝔽₈)×C₅₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
9	D₇×C₅₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
10	C₁₃×C₅₉	AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Hall
11	C₁₃×AGL(1,𝔽₇)	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₅₉	—	7	1	no	Hall
14	C₁₃×ΓL(1,𝔽₈)	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
15	C₁₃×D₇	C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅₉	—	7	1	no	Hall
17	C₂×C₅₉	—	7	1	no	Hall
18	C₇×C₁₃	C₂×C₃×C₅₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₁₃	—	7	1	no	Hall
20	C₅₉	C₁₃×AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
21	AGL(1,𝔽₇)	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
22	C₃×C₁₃	—	7	1	no	Hall
23	C₂×C₁₃	—	7	1	no	Hall
24	ΓL(1,𝔽₈)	C₂×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Hall
25	D₇	C₃×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Hall
26	C₁₃	AGL(1,𝔽₇)×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₃×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	7	1	no	Hall
29	C₃	—	7	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₅₉	AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₅₉	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₃×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×ΓL(1,𝔽₈)×C₅₉	C₂	semidirect
2. C₁₃×D₇×C₅₉	C₃	semidirect
3. C₇×C₁₃×C₅₉	C₂×C₃	semidirect
5. AGL(1,𝔽₇)×C₅₉	C₁₃	direct (N × H)
8. ΓL(1,𝔽₈)×C₅₉	C₂×C₁₃	semidirect
9. D₇×C₅₉	C₃×C₁₃	semidirect
10. C₁₃×C₅₉	AGL(1,𝔽₇)	direct (N × H)
11. C₁₃×AGL(1,𝔽₇)	C₅₉	direct (N × H)
12. C₇×C₅₉	C₂×C₃×C₁₃	semidirect
14. C₁₃×ΓL(1,𝔽₈)	C₂×C₅₉	semidirect
15. C₁₃×D₇	C₃×C₅₉	semidirect
18. C₇×C₁₃	C₂×C₃×C₅₉	semidirect
20. C₅₉	C₁₃×AGL(1,𝔽₇)	direct (N × H)
21. AGL(1,𝔽₇)	C₁₃×C₅₉	direct (N × H)
24. ΓL(1,𝔽₈)	C₂×C₁₃×C₅₉	semidirect
25. D₇	C₃×C₁₃×C₅₉	semidirect
26. C₁₃	AGL(1,𝔽₇)×C₅₉	direct (N × H)
27. C₇	C₂×C₃×C₁₃×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×ΓL(1,𝔽₈)×C₅₉	2
C₁₃×D₇×C₅₉	3
C₂×C₃×C₁₃×C₅₉	7
AGL(1,𝔽₇)×C₅₉	13
C₁₃×AGL(1,𝔽₇)	59

Subgroups — C13×AGL(1,𝔽7)×C59 #44567280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×AGL(1,𝔽₇)×C₅₉ #44567280