Subgroups — C₂×C₅×D₂₁ #88313

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	C₅×D₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₇	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₇	D₃	1	1	yes	characteristic, complemented
7	C₅×D₇	—	3	2	no	—
8	C₂×C₅×D₃	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	C₂×C₅	1	1	yes	characteristic, complemented
10	D₂₁	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅	D₇	1	1	yes	characteristic, complemented
13	C₅×D₃	—	7	2	no	—
14	C₂×D₇	—	3	1	no	Hall
15	C₃×C₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂²×C₅	—	21	1	no	Hall
17	C₃×C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇	C₅×D₃	1	1	yes	characteristic, complemented
19	D₇	—	3	2	no	—
20	C₂×D₃	—	7	1	no	Hall
21	C₂×C₅	—	21	2	no	—
22	C₂×C₅	D₂₁	1	1	yes	characteristic, direct product factor
23	C₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	C₅×D₇	1	1	yes	characteristic, complemented
25	D₃	—	7	2	no	—
26	C₅	C₂×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	21	1	no	Sylow
28	C₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	21	2	no	—
30	C₂	C₅×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₅

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.