Subgroups — #49180643

Order 37820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22628162	C₂	1	1	yes	maximal, characteristic
2	#22628162	C₄	1	1	yes	characteristic, complemented, Hall
3	C₆₁×Dic₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₃₁×C₆₁	C₂×C₅	1	1	yes	characteristic
5	C₃₁×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
6	C₄×C₆₁⋊C₅	—	31	1	no	maximal, Hall
7	Dic₃₁⋊C₅	—	61	1	no	maximal, Hall
8	C₂×C₆₁⋊C₅	—	31	1	no	—
9	C₂×ΓL(1,𝔽₃₂)	—	61	1	no	—
10	C₆₁⋊C₅	—	31	1	no	Hall
11	C₄×C₆₁	—	31	1	no	Hall
12	ΓL(1,𝔽₃₂)	—	61	1	no	Hall
13	Dic₃₁	C₆₁⋊C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₆₁	D₃₁⋊C₅	1	1	yes	characteristic
15	C₂×C₃₁	C₂×C₆₁⋊C₅	1	1	yes	characteristic
16	C₆₁	Dic₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	C₄×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1891	1	no	Hall
19	C₂×C₅	—	1891	1	no	—
20	C₅	—	1891	1	no	Sylow
21	C₄	—	31	1	no	Sylow
22	C₂	#34038663	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#34038663
commutator, hypocenter	C₃₁×C₆₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₃₁×C₆₁	C₂×C₅
prime radical	C₂×#22628162	C₂
LCS	G ▷ C₃₁×C₆₁
UCS	C₁ ◁ C₂

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.