Subgroups — #63305

Order 280.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₇	C₂²	1	1	yes	characteristic
5	C₅×D₇	—	2	1	no	—
6	C₇×D₅	—	2	1	no	—
7	C₂²⋊D₇	—	5	1	no	maximal, Hall
8	C₂²⋊D₅	—	7	1	no	maximal, Hall
9	C₅×C₇	D₄	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₇	—	5	1	no	—
11	C₂×D₇	D₅	1	1	yes	characteristic, complemented
12	Dic₇	—	5	1	no	—
13	C₂²×C₅	—	7	1	no	—
14	C₂×D₅	D₇	1	1	yes	characteristic, complemented
15	Dic₅	—	7	1	no	—
16	C₂×C₇	—	10	1	no	—
17	C₂×C₇	C₂×D₅	1	1	yes	characteristic
18	D₇	—	2	1	no	—
19	C₂×C₅	—	14	1	no	—
20	C₂×C₅	C₂×D₇	1	1	yes	characteristic
21	D₅	—	2	1	no	—
22	D₄	—	35	1	no	Sylow
23	C₇	C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
24	C₅	C₂²⋊D₇	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	5	1	no	—
26	C₂²	—	7	1	no	—
27	C₄	—	35	1	no	—
28	C₂	—	10	1	no	—
29	C₂	—	14	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.