Subgroups — D₅×D₂₁ #88303

Order 420.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₂₁	—	5	1	no	maximal, Hall
7	D₃₅	—	3	1	no	—
8	C₅×D₇	—	3	1	no	—
9	C₇×D₅	D₃	1	1	yes	characteristic, complemented
10	D₃×D₅	—	7	1	no	maximal, Hall
11	C₂×C₃×C₇	—	5	1	no	—
12	D₂₁	—	5	1	no	—
13	D₂₁	D₅	1	1	yes	characteristic, direct product factor
14	C₅×C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₅	—	7	1	no	—
16	C₃×D₅	D₇	1	1	yes	characteristic, complemented
17	C₅×D₃	—	7	1	no	—
18	C₂×D₇	—	15	1	no	Hall
19	C₃×C₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×D₅	—	21	1	no	Hall
21	C₃×C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₇	—	5	1	no	—
23	D₇	—	3	1	no	—
24	D₇	—	15	1	no	—
25	C₂×D₃	—	35	1	no	Hall
26	C₂×C₅	—	21	1	no	—
27	D₅	—	21	1	no	—
28	D₅	D₂₁	1	1	yes	characteristic, direct product factor
29	C₇	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	—	5	1	no	—
31	D₃	—	7	1	no	—
32	D₃	—	35	1	no	—
33	C₅	C₂×D₂₁	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	105	1	no	Sylow
35	C₃	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	5	1	no	—
37	C₂	—	21	1	no	—
38	C₂	—	105	1	no	—

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

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.