Subgroups — C₂×C₇×5₋¹⁺² #13182090

Order 1750.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×5₋¹⁺²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₇	C₅	1	1	yes	maximal, characteristic
3	C₂×C₇×C₂₅	C₅	1	5	yes	maximal, complemented
4	C₂×5₋¹⁺²	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅²×C₇	C₂×C₅	1	1	yes	characteristic
6	C₇×C₂₅	C₂×C₅	1	5	yes	complemented
7	5₋¹⁺²	C₂×C₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₅×C₇	—	5	1	no	—
9	C₂×C₅×C₇	C₅²	1	1	yes	characteristic
10	C₂×C₅²	C₅×C₇	1	1	yes	characteristic
11	C₂×C₂₅	C₅×C₇	1	5	yes	complemented
12	C₅×C₇	—	5	1	no	—
13	C₅×C₇	C₂×C₅²	1	1	yes	characteristic
14	C₅²	C₂×C₅×C₇	1	1	yes	characteristic
15	C₂₅	C₂×C₅×C₇	1	5	yes	complemented
16	C₂×C₇	5₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅	—	5	1	no	—
18	C₂×C₅	C₅²×C₇	1	1	yes	characteristic
19	C₇	C₂×5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
20	C₅	—	5	1	no	—
21	C₅	C₂×C₅²×C₇	1	1	yes	characteristic
22	C₂	C₇×5₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₅×C₇	C₅²
commutator, Frattini, cosocle	C₅	C₂×C₅²×C₇
prime radical	C₂×C₅²×C₇	C₅
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₇ ◁ G

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.