Subgroups — C₂×D₈₄₃₅ #46798124

Order 33740.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₂₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₆₈₇	—	5	1	no	maximal, Hall
5	C₂×D₁₂₀₅	—	7	1	no	maximal, Hall
6	C₂×C₇×C₂₄₁	D₅	1	1	yes	characteristic, complemented
7	D₁₆₈₇	—	5	2	no	—
8	C₂×C₅×C₂₄₁	D₇	1	1	yes	characteristic, complemented
9	D₁₂₀₅	—	7	2	no	—
10	C₇×C₂₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₂₄₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₂₄₁	—	35	1	no	Hall
13	C₂×C₂₄₁	D₃₅	1	1	yes	characteristic, complemented
14	D₂₄₁	—	35	2	no	—
15	C₂₄₁	C₂×D₃₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₃₅	—	241	1	no	maximal, Hall
17	C₂×C₅×C₇	D₂₄₁	1	1	yes	characteristic, complemented
18	D₃₅	—	241	2	no	—
19	C₅×C₇	C₂×D₂₄₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	1205	1	no	Hall
21	C₂×D₅	—	1687	1	no	Hall
22	C₂×C₇	D₁₂₀₅	1	1	yes	characteristic, complemented
23	D₇	—	1205	2	no	—
24	C₂×C₅	D₁₆₈₇	1	1	yes	characteristic, complemented
25	D₅	—	1687	2	no	—
26	C₇	C₂×D₁₂₀₅	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₁₆₈₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	8435	1	no	Sylow
29	C₂	—	8435	2	no	—
30	C₂	D₈₄₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₄₃₅
commutator, cosocle, hypocenter	C₅×C₇×C₂₄₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₂₄₁	C₂
LCS	G ▷ C₅×C₇×C₂₄₁
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.