Subgroups — ΓL(1,𝔽₈)⋊(D₁₅₁⋊C₅) #44540301

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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