Subgroups — C₅⋊(ΓL(1,𝔽₈)⋊D₁₅₁) #44540289

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×ΓL(1,𝔽₈)×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₈₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)⋊D₁₅₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₇₅₅	—	7	1	no	maximal, Hall
6	ΓL(1,𝔽₈)×C₁₅₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	—	7	1	no	Hall
8	D₁₀₅₇	—	5	1	no	Hall
9	D₇₅₅	—	7	1	no	Hall
10	C₇×C₁₅₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₅₁	—	35	1	no	Hall
12	C₅×C₁₅₁	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	—	7	1	no	Hall
14	D₁₅₁	—	35	1	no	Hall
15	C₅⋊AGL(1,𝔽₇)	—	151	1	no	maximal, Hall
16	C₁₅₁	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
17	C₅×ΓL(1,𝔽₈)	D₁₅₁	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	151	1	no	Hall
19	AGL(1,𝔽₇)	—	755	1	no	Hall
20	C₅×C₇	C₃×D₁₅₁	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	1057	1	no	Hall
22	ΓL(1,𝔽₈)	D₇₅₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	—	7	1	no	Hall
24	D₇	—	755	1	no	Hall
25	D₅	—	1057	1	no	Hall
26	C₇	C₃×D₇₅₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	5285	1	no	Hall
28	C₅	ΓL(1,𝔽₈)⋊D₁₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	7	1	no	Sylow
30	C₂	—	5285	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₅₁	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₅₁
UCS	C₁

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

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