Subgroups — #63306

Order 280.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
5	D₃₅	—	2	1	no	—
6	C₅×D₇	—	2	1	no	—
7	D₂₈	—	5	1	no	maximal, Hall
8	C₂²⋊D₅	—	7	1	no	maximal, Hall
9	C₅×C₇	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂×D₇	—	5	1	no	—
11	C₂×D₇	D₅	1	1	yes	characteristic, complemented
12	C₄×C₇	—	5	1	no	—
13	C₂²×C₅	—	7	1	no	—
14	C₂×D₅	—	7	1	no	—
15	Dic₅	D₇	1	1	yes	characteristic, complemented
16	C₂×C₇	C₂×D₅	1	1	yes	characteristic
17	D₇	—	2	1	no	—
18	D₇	—	10	1	no	—
19	C₂×C₅	—	14	1	no	—
20	C₂×C₅	C₂×D₇	1	1	yes	characteristic
21	D₅	—	14	1	no	—
22	D₄	—	35	1	no	Sylow
23	C₇	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
24	C₅	D₂₈	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	7	1	no	—
26	C₂²	—	35	1	no	—
27	C₄	—	5	1	no	—
28	C₂	—	14	1	no	—
29	C₂	—	70	1	no	—
30	C₂	D₅×D₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×D₇
commutator, Fitting, socle, cosocle	C₂×C₅×C₇	C₂²
hypocenter	C₅×C₇	D₄
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.