Subgroups — #46777421

Order 33620.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681142	C₂	1	1	yes	maximal, characteristic
2	#22554262	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269606	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₁×D₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄₁²	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
6	#4223⋊C₅	—	41	1	no	maximal
7	Dic₄₁⋊C₅	—	41	1	no	maximal
8	C₂×C₄₁⋊C₅	—	41	1	no	—
9	D₄₁⋊C₅	—	41	1	no	—
10	C₄₁⋊C₅	—	41	1	no	—
11	C₄₁⋊C₅	—	41	1	no	—
12	#4223	—	41	1	no	—
13	Dic₄₁	—	41	1	no	—
14	C₂×C₄₁	—	41	1	no	—
15	D₄₁	D₄₁⋊C₅	1	1	yes	characteristic
16	C₄₁	—	20	2	no	—
17	C₄₁	Dic₄₁⋊C₅	1	1	yes	characteristic, complemented
18	C₄₁	#4223⋊C₅	1	1	yes	characteristic, complemented
19	C₄×C₅	—	1681	1	no	Hall
20	C₂×C₅	—	1681	1	no	—
21	C₅	—	1681	1	no	Sylow
22	C₄	—	1681	1	no	Sylow
23	C₂	—	41	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₁²	C₄×C₅
prime radical	#30681142	C₂
cosocle	C₄₁×D₄₁	C₂×C₅
LCS	G ▷ 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.