Subgroups — #63308

Order 280.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₅	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₇×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
5	Dic₁₄	—	5	1	no	maximal, Hall
6	Dic₁₀	—	7	1	no	maximal, Hall
7	C₅×C₇	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₄×C₇	—	5	1	no	—
9	Dic₇	—	5	1	no	—
10	Dic₇	D₅	1	1	yes	characteristic
11	C₄×C₅	—	7	1	no	—
12	Dic₅	—	7	1	no	—
13	Dic₅	D₇	1	1	yes	characteristic
14	C₂×C₇	C₂×D₅	1	1	yes	characteristic
15	C₂×C₅	C₂×D₇	1	1	yes	characteristic
16	Q₈	—	35	1	no	Sylow
17	C₇	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
18	C₅	Dic₁₄	1	1	yes	characteristic, complemented, Sylow
19	C₄	—	5	1	no	—
20	C₄	—	7	1	no	—
21	C₄	—	35	1	no	—
22	C₂	D₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₇
commutator, Fitting, socle, prime radical, cosocle	C₂×C₅×C₇	C₂²
hypocenter	C₅×C₇	Q₈
LCS	G ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂

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.