Subgroups — D₇×5₋¹⁺² #13182075

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, complemented, Hall
2	C₅²×D₇	C₅	1	1	yes	maximal, characteristic
3	D₇×C₂₅	C₅	1	5	yes	maximal, complemented
4	C₂×5₋¹⁺²	—	7	1	no	maximal, Hall
5	C₅²×C₇	C₂×C₅	1	1	yes	characteristic
6	C₇×C₂₅	C₂×C₅	1	5	yes	complemented
7	5₋¹⁺²	D₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₅×D₇	—	5	1	no	—
9	C₅×D₇	C₅²	1	1	yes	characteristic
10	C₂×C₅²	—	7	1	no	—
11	C₂×C₂₅	—	7	5	no	—
12	C₅×C₇	—	5	1	no	—
13	C₅×C₇	C₂×C₅²	1	1	yes	characteristic
14	C₅²	C₅×D₇	1	1	yes	characteristic
15	C₂₅	C₅×D₇	1	5	yes	complemented
16	D₇	5₋¹⁺²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅	—	7	1	no	—
18	C₂×C₅	—	35	1	no	—
19	C₇	C₂×5₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
20	C₅	—	5	1	no	—
21	C₅	C₅²×D₇	1	1	yes	characteristic
22	C₂	—	7	1	no	Sylow

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.