Subgroups — C₅×D₄₁² #46777451

Order 33620.

120 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	C₅×C₄₁×D₄₁	C₂	1	2	yes	maximal, complemented
3	C₅×C₄₁²	C₂²	1	1	yes	characteristic, complemented, Hall
4	D₄₁²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄₁⋊D₄₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₄₁×D₄₁	C₂×C₅	1	2	yes	complemented
7	C₄₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₅×D₄₁	—	41	2	no	maximal
9	C₂×C₅×C₄₁	—	41	2	no	—
10	C₅×D₄₁	—	41	2	no	—
11	C₅×D₄₁	—	82	20	no	—
12	C₅×D₄₁	D₄₁	1	2	yes	direct product factor
13	C₅×C₄₁	—	2	20	no	—
14	C₅×C₄₁	C₂×D₄₁	1	2	yes	complemented
15	C₂×D₄₁	—	41	2	no	—
16	C₂×C₄₁	—	41	2	no	—
17	D₄₁	—	41	2	no	—
18	D₄₁	—	82	20	no	—
19	D₄₁	C₅×D₄₁	1	2	yes	direct product factor
20	C₄₁	—	2	20	no	—
21	C₄₁	C₂×C₅×D₄₁	1	2	yes	complemented
22	C₂²×C₅	—	1681	1	no	Hall
23	C₂×C₅	—	41	2	no	—
24	C₂×C₅	—	1681	1	no	—
25	C₅	D₄₁²	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	—	1681	1	no	Sylow
27	C₂	—	41	2	no	—
28	C₂	—	1681	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₄₁²
commutator, cosocle, hypocenter	C₄₁²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₄₁²	C₂²
LCS	G ▷ C₄₁²
UCS	C₁ ◁ 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.