Subgroups — C₂×C₃×D₃₅ #88311

Order 420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₇	—	5	1	no	maximal, Hall
6	C₂×C₅×C₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×D₅	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	D₅	1	1	yes	characteristic, complemented
10	C₃×D₇	—	5	2	no	—
11	C₅×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅	D₇	1	1	yes	characteristic, complemented
13	C₃×D₅	—	7	2	no	—
14	C₂×D₇	—	5	1	no	Hall
15	C₃×C₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₅	—	7	1	no	Hall
17	C₃×C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇	C₃×D₅	1	1	yes	characteristic, complemented
19	D₇	—	5	2	no	—
20	C₂²×C₃	—	35	1	no	Hall
21	C₂×C₅	C₃×D₇	1	1	yes	characteristic, complemented
22	D₅	—	7	2	no	—
23	C₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	35	2	no	—
25	C₂×C₃	D₃₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	35	1	no	Sylow
28	C₃	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	35	2	no	—
30	C₂	C₃×D₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₃

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.