Subgroups — C₂×D₅₁₅₁ #35207276

Order 20604.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₇×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₇₁₇	—	3	1	no	maximal, Hall
4	C₃×C₁₇×C₁₀₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×C₁₀₁	D₃	1	1	yes	characteristic, complemented
6	D₁₇₁₇	—	3	2	no	—
7	C₁₇×C₁₀₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₀₃	—	17	1	no	maximal, Hall
9	C₂×C₃×C₁₀₁	D₁₇	1	1	yes	characteristic, complemented
10	D₃₀₃	—	17	2	no	—
11	C₂×D₁₀₁	—	51	1	no	Hall
12	C₃×C₁₀₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×D₅₁	—	101	1	no	maximal, Hall
14	C₂×C₁₀₁	D₅₁	1	1	yes	characteristic, complemented
15	D₁₀₁	—	51	2	no	—
16	C₂×C₃×C₁₇	D₁₀₁	1	1	yes	characteristic, complemented
17	D₅₁	—	101	2	no	—
18	C₁₀₁	C₂×D₅₁	1	1	yes	characteristic, complemented, Sylow
19	C₂×D₁₇	—	303	1	no	Hall
20	C₃×C₁₇	C₂×D₁₀₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₇	D₃₀₃	1	1	yes	characteristic, complemented
22	D₁₇	—	303	2	no	—
23	C₁₇	C₂×D₃₀₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₃	—	1717	1	no	Hall
25	C₂×C₃	D₁₇₁₇	1	1	yes	characteristic, complemented
26	D₃	—	1717	2	no	—
27	C₂²	—	5151	1	no	Sylow
28	C₃	C₂×D₁₇₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	5151	2	no	—
30	C₂	D₅₁₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₅₁₅₁
commutator, cosocle, hypocenter	C₃×C₁₇×C₁₀₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇×C₁₀₁	C₂
LCS	G ▷ C₃×C₁₇×C₁₀₁
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.