Subgroups — C₇×C₃₁×C₅⋊D₅ #24925762

Order 10850.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₃₁	—	5	6	no	maximal
3	C₃₁×C₅⋊D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₃₁	D₅	1	6	yes	complemented
5	C₅²×C₃₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₂×C₇×C₃₁	—	25	1	no	Hall
7	C₇×C₅⋊D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	D₅×C₃₁	—	5	6	no	—
9	C₇×C₃₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
10	C₅²×C₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₁	C₇×D₅	1	6	yes	complemented
12	C₇×D₅	—	5	6	no	—
13	C₂×C₃₁	—	25	1	no	Hall
14	C₅⋊D₅	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₇	D₅×C₃₁	1	6	yes	complemented
16	C₃₁	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₅²	C₂×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₇	—	25	1	no	Hall
19	D₅	—	5	6	no	—
20	C₇	C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₅	C₇×D₅×C₃₁	1	6	yes	complemented
22	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇×C₃₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₃₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₇×C₃₁

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.