Subgroups — D₅×C₄₁⋊D₄₁ #46777469

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	1	yes	maximal, characteristic, complemented
2	D₅×C₄₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₁⋊D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₄₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₁⋊D₄₁	—	5	1	no	maximal, Hall
6	C₂×C₄₁²	—	5	1	no	—
7	C₄₁⋊D₄₁	—	5	1	no	—
8	C₄₁⋊D₄₁	D₅	1	1	yes	characteristic, direct product factor
9	C₄₁²	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
10	D₅×D₄₁	—	41	42	no	maximal
11	D₂₀₅	—	41	42	no	—
12	C₅×D₄₁	—	41	42	no	—
13	D₅×C₄₁	D₄₁	1	42	yes	complemented
14	C₅×C₄₁	C₂×D₄₁	1	42	yes	complemented
15	C₂×D₄₁	—	205	42	no	—
16	C₂×C₄₁	—	5	42	no	—
17	D₄₁	—	41	42	no	—
18	D₄₁	—	205	42	no	—
19	C₄₁	D₅×D₄₁	1	42	yes	complemented
20	C₂×D₅	—	1681	1	no	Hall
21	C₂×C₅	—	1681	1	no	—
22	D₅	—	1681	1	no	—
23	D₅	C₄₁⋊D₄₁	1	1	yes	characteristic, direct product factor
24	C₅	C₂×C₄₁⋊D₄₁	1	1	yes	characteristic, complemented, Sylow
25	C₂²	—	8405	1	no	Sylow
26	C₂	—	5	1	no	—
27	C₂	—	1681	1	no	—
28	C₂	—	8405	1	no	—

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