Subgroups — #20263623⋊C₅ #44540294

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15691748⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₅₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#20263623	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₁₅₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	(D₁₅₁⋊C₃)⋊C₅	—	7	1	no	maximal, Hall
6	#15691748	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	(C₁₅₁⋊C₃)⋊C₅	—	7	1	no	Hall
8	C₇×D₁₅₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	D₁₅₁⋊C₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	D₁₅₁⋊C₃	—	7	1	no	Hall
12	C₁₅₁⋊C₅	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₁₅₁⋊C₃	—	7	1	no	Hall
14	D₁₅₁	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×ΓL(1,𝔽₈)	—	151	1	no	maximal, Hall
16	C₁₅₁	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
17	C₅×ΓL(1,𝔽₈)	—	151	1	no	Hall
18	C₂×C₅×C₇	—	151	1	no	Hall
19	C₂×ΓL(1,𝔽₈)	—	151	1	no	Hall
20	C₅×C₇	—	151	1	no	Hall
21	C₂×C₃×C₅	—	1057	1	no	Hall
22	ΓL(1,𝔽₈)	—	151	1	no	Hall
23	C₃×C₅	—	1057	1	no	Hall
24	C₂×C₇	—	151	1	no	Hall
25	C₂×C₅	—	151	1	no	Hall
26	C₇	(D₁₅₁⋊C₃)⋊C₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	1057	1	no	Hall
28	C₅	—	151	1	no	Sylow
29	C₃	—	1057	1	no	Sylow
30	C₂	—	151	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.