Subgroups — D₅×ΓL(1,𝔽₈)×C₁₄₉ #44530985

Order 31290.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×ΓL(1,𝔽₈)×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₁₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×ΓL(1,𝔽₈)×C₁₄₉	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅×C₁₄₉	—	7	1	no	maximal, Hall
6	ΓL(1,𝔽₈)×C₁₄₉	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×C₁₄₉	—	7	1	no	Hall
8	C₂×C₇×C₁₄₉	—	5	1	no	Hall
9	D₅×C₁₄₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₄₉	—	35	1	no	Hall
12	C₅×C₁₄₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₄₉	—	7	1	no	Hall
14	C₂×C₁₄₉	—	5	1	no	Hall
15	D₅×ΓL(1,𝔽₈)	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₄₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
17	C₅×ΓL(1,𝔽₈)	C₂×C₁₄₉	1	1	yes	characteristic, complemented, Hall
18	C₇×D₅	C₃×C₁₄₉	1	1	yes	characteristic, complemented, Hall
19	C₂×ΓL(1,𝔽₈)	—	5	1	no	Hall
20	C₅×C₇	C₂×C₃×C₁₄₉	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	7	1	no	Hall
22	ΓL(1,𝔽₈)	D₅×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	—	7	1	no	Hall
24	C₂×C₇	—	5	1	no	Hall
25	D₅	ΓL(1,𝔽₈)×C₁₄₉	1	1	yes	characteristic, direct product factor, Hall
26	C₇	C₃×D₅×C₁₄₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	35	1	no	Hall
28	C₅	C₂×ΓL(1,𝔽₈)×C₁₄₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	7	1	no	Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₄₉	D₅×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃×C₁₄₉
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₄₉	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₁₄₉

Complements

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

N	H ≅ G/N	type
1. C₅×ΓL(1,𝔽₈)×C₁₄₉	C₂	semidirect
2. C₇×D₅×C₁₄₉	C₃	semidirect
4. C₅×C₇×C₁₄₉	C₂×C₃	semidirect
6. ΓL(1,𝔽₈)×C₁₄₉	D₅	direct (N × H)
9. D₅×C₁₄₉	ΓL(1,𝔽₈)	direct (N × H)
10. C₇×C₁₄₉	C₃×D₅	semidirect
12. C₅×C₁₄₉	C₂×ΓL(1,𝔽₈)	semidirect
15. D₅×ΓL(1,𝔽₈)	C₁₄₉	direct (N × H)
16. C₁₄₉	D₅×ΓL(1,𝔽₈)	direct (N × H)
17. C₅×ΓL(1,𝔽₈)	C₂×C₁₄₉	semidirect
18. C₇×D₅	C₃×C₁₄₉	semidirect
20. C₅×C₇	C₂×C₃×C₁₄₉	semidirect
22. ΓL(1,𝔽₈)	D₅×C₁₄₉	direct (N × H)
25. D₅	ΓL(1,𝔽₈)×C₁₄₉	direct (N × H)
26. C₇	C₃×D₅×C₁₄₉	semidirect
28. C₅	C₂×ΓL(1,𝔽₈)×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×ΓL(1,𝔽₈)×C₁₄₉	2
C₇×D₅×C₁₄₉	3
C₂×ΓL(1,𝔽₈)×C₁₄₉	5
C₃×D₅×C₁₄₉	7
D₅×ΓL(1,𝔽₈)	149

Subgroups — D5×ΓL(1,𝔽8)×C149 #44530985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×ΓL(1,𝔽₈)×C₁₄₉ #44530985