Subgroups — C₅×C₇⋊(D₃₁⋊C₅) #24925752

Order 10850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊(D₃₁⋊C₅)	C₅	1	5	yes	maximal, direct product factor
3	C₅×D₂₁₇	C₅	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃₁⋊C₅	—	7	1	no	maximal, Hall
5	C₅×C₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₇×ΓL(1,𝔽₃₂)	C₂×C₅	1	5	yes	complemented
7	C₅×ΓL(1,𝔽₃₂)	D₇	1	1	yes	characteristic, complemented, Hall
8	D₂₁₇	C₅²	1	1	yes	characteristic, complemented, Hall
9	C₅²×D₇	—	31	1	no	maximal, Hall
10	C₅×D₃₁	—	7	1	no	—
11	D₃₁⋊C₅	—	7	5	no	—
12	C₇×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅²×C₇	—	31	1	no	Hall
14	C₅×C₃₁	C₅×D₇	1	1	yes	characteristic, complemented
15	ΓL(1,𝔽₃₂)	C₅×D₇	1	5	yes	complemented
16	C₅×D₇	—	31	5	no	—
17	C₅×D₇	—	31	1	no	—
18	D₃₁	—	7	1	no	Hall
19	C₂×C₅²	—	217	1	no	Hall
20	C₅×C₇	—	31	5	no	—
21	C₅×C₇	D₃₁⋊C₅	1	1	yes	characteristic, complemented
22	C₃₁	C₅²×D₇	1	1	yes	characteristic, complemented, Sylow
23	C₅²	—	31	1	no	Sylow
24	D₇	—	31	1	no	Hall
25	C₂×C₅	—	217	5	no	—
26	C₂×C₅	—	217	1	no	—
27	C₇	C₅×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
28	C₅	—	31	5	no	—
29	C₅	C₇⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
30	C₂	—	217	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₇⋊(D₃₁⋊C₅)
commutator, cosocle, hypocenter	C₇×C₃₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₃₁	C₂×C₅
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₅

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.