Subgroups — C₂×D₂₁×C₇₁ #20238564

Order 5964.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₁×C₇₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₇×C₇₁	—	3	1	no	maximal, Hall
4	C₃×C₇×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₇₁	D₃	1	1	yes	characteristic, complemented
6	D₇×C₇₁	—	3	2	no	—
7	C₂×D₃×C₇₁	—	7	1	no	maximal, Hall
8	C₇×C₇₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇₁	D₇	1	1	yes	characteristic, complemented
10	D₃×C₇₁	—	7	2	no	—
11	C₂²×C₇₁	—	21	1	no	Hall
12	C₃×C₇₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇₁	—	21	2	no	—
14	C₂×C₇₁	D₂₁	1	1	yes	characteristic, direct product factor
15	C₂×D₂₁	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₇₁	C₂×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃×C₇	C₂×C₇₁	1	1	yes	characteristic, complemented
18	D₂₁	C₂×C₇₁	1	2	yes	direct product factor
19	C₂×D₇	—	3	1	no	Hall
20	C₃×C₇	C₂²×C₇₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇	D₃×C₇₁	1	1	yes	characteristic, complemented
22	D₇	—	3	2	no	—
23	C₂×D₃	—	7	1	no	Hall
24	C₇	C₂×D₃×C₇₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	D₇×C₇₁	1	1	yes	characteristic, complemented
26	D₃	—	7	2	no	—
27	C₂²	—	21	1	no	Sylow
28	C₃	C₂×D₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	21	2	no	—
30	C₂	D₂₁×C₇₁	1	1	yes	characteristic, direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.