Subgroups — #46777471

Order 33620.

104 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
2	C₅×C₄₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269609	—	5	1	no	maximal, Hall
4	C₄₁⋊D₄₁	D₅	1	1	yes	characteristic
5	C₄₁²	Dic₅	1	1	yes	characteristic, complemented, Sylow
6	#11717964	—	41	2	no	maximal
7	C₅×D₄₁	—	41	2	no	—
8	C₅×D₄₁	—	82	20	no	—
9	C₅×C₄₁	—	2	20	no	—
10	C₅×C₄₁	#4223	1	2	yes	complemented
11	#4223	—	205	2	no	—
12	D₄₁	—	41	2	no	—
13	D₄₁	—	82	20	no	—
14	C₄₁	—	2	20	no	—
15	C₄₁	#11717964	1	2	yes	complemented
16	Dic₅	—	1681	1	no	Hall
17	C₂×C₅	—	1681	1	no	—
18	C₅	#20269609	1	1	yes	characteristic, complemented, Sylow
19	C₄	—	8405	1	no	Sylow
20	C₂	—	1681	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₄₁²	C₄
prime radical, cosocle	C₅×C₄₁⋊D₄₁	C₂
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.