Subgroups — C₂×C₅×C₄₁⋊D₄₁ #46777473

Order 33620.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₁⋊D₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₄₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₁²	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₁⋊D₄₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₄₁²	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₁⋊D₄₁	C₂×C₅	1	2	yes	direct product factor
7	C₄₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×D₄₁	—	41	42	no	maximal
9	C₂×C₅×C₄₁	D₄₁	1	42	yes	complemented
10	C₅×D₄₁	—	41	84	no	—
11	C₅×C₄₁	C₂×D₄₁	1	42	yes	complemented
12	C₂×D₄₁	—	41	42	no	—
13	C₂×C₄₁	C₅×D₄₁	1	42	yes	complemented
14	D₄₁	—	41	84	no	—
15	C₄₁	C₂×C₅×D₄₁	1	42	yes	complemented
16	C₂²×C₅	—	1681	1	no	Hall
17	C₂×C₅	—	1681	2	no	—
18	C₂×C₅	C₄₁⋊D₄₁	1	1	yes	characteristic, direct product factor
19	C₅	C₂×C₄₁⋊D₄₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂²	—	1681	1	no	Sylow
21	C₂	—	1681	2	no	—
22	C₂	C₅×C₄₁⋊D₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₄₁⋊D₄₁
commutator, cosocle, hypocenter	C₄₁²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₄₁²	C₂
LCS	G ▷ C₄₁²
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.