Subgroups — #46777458

Order 33620.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₂₀₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269606	—	5	1	no	maximal, Hall
4	C₄₁×D₄₁	—	5	1	no	—
5	C₄₁²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	#11717963	—	41	1	no	maximal
7	#11717961	—	41	1	no	maximal
8	D₂₀₅	D₄₁	1	1	yes	characteristic
9	D₅×C₄₁	—	41	1	no	—
10	C₅×C₄₁	—	4	10	no	—
11	C₅×C₄₁	Dic₄₁	1	1	yes	characteristic, complemented
12	C₅×C₄₁	#4223	1	1	yes	characteristic, complemented
13	#4223	—	205	1	no	—
14	Dic₄₁	—	205	1	no	—
15	C₂×C₄₁	—	205	1	no	—
16	D₄₁	—	5	1	no	—
17	C₄₁	—	4	10	no	—
18	C₄₁	#11717961	1	1	yes	characteristic, complemented
19	C₄₁	#11717963	1	1	yes	characteristic, complemented
20	AGL(1,𝔽₅)	—	1681	1	no	Hall
21	D₅	—	41	1	no	—
22	C₅	#20269606	1	1	yes	characteristic, complemented, Sylow
23	C₄	—	8405	1	no	Sylow
24	C₂	—	205	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₄₁²	C₄
prime radical, cosocle	C₄₁×D₂₀₅	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.