Subgroups — C₅⋊#17987079 #37504355

Order 22890.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14556233	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#17987079	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅⋊(D₁₀₉⋊C₃)	—	7	1	no	maximal, Hall
6	#14556233	D₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₀₉⋊C₃	—	7	1	no	Hall
8	C₇×D₁₀₉	—	5	1	no	Hall
9	D₅₄₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₀₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	D₁₀₉⋊C₃	—	35	1	no	Hall
12	C₅×C₁₀₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₁₀₉⋊C₃	—	7	1	no	Hall
14	D₁₀₉	—	5	1	no	Hall
15	D₅×ΓL(1,𝔽₈)	—	109	1	no	maximal, Hall
16	C₁₀₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
17	C₅×ΓL(1,𝔽₈)	—	109	1	no	Hall
18	C₇×D₅	—	327	1	no	Hall
19	C₂×ΓL(1,𝔽₈)	—	545	1	no	Hall
20	C₅×C₇	D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	763	1	no	Hall
22	ΓL(1,𝔽₈)	—	109	1	no	Hall
23	C₃×C₅	—	763	1	no	Hall
24	C₂×C₇	—	1635	1	no	Hall
25	D₅	—	327	1	no	Hall
26	C₇	C₅⋊(D₁₀₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3815	1	no	Hall
28	C₅	#17987079	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	763	1	no	Sylow
30	C₂	—	1635	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₇×C₁₀₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₀₉
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.