Subgroups — C₂×#34038658 #49180686

Order 37820.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#34038658	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22628160	C₂	1	1	yes	maximal, characteristic, complemented
3	#22628160	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃₁×D₆₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃₁×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented
6	C₃₁×D₆₁	C₂×C₅	1	2	yes	complemented
7	C₃₁×C₆₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₆₁⋊C₅	—	31	1	no	maximal, Hall
9	C₂²×ΓL(1,𝔽₃₂)	—	61	1	no	maximal, Hall
10	C₂×C₆₁⋊C₅	—	31	1	no	—
11	D₆₁⋊C₅	—	31	2	no	—
12	C₂×ΓL(1,𝔽₃₂)	—	61	2	no	—
13	C₂×ΓL(1,𝔽₃₂)	—	61	1	no	—
14	C₆₁⋊C₅	—	31	1	no	Hall
15	C₂×D₆₁	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Hall
16	ΓL(1,𝔽₃₂)	—	61	1	no	Hall
17	C₂²×C₃₁	—	61	1	no	Hall
18	C₂×C₆₁	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
19	D₆₁	C₂×ΓL(1,𝔽₃₂)	1	2	yes	complemented
20	C₂×C₃₁	—	61	2	no	—
21	C₂×C₃₁	D₆₁⋊C₅	1	1	yes	characteristic, complemented
22	C₆₁	C₂²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
23	C₃₁	C₂×D₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₅	—	1891	1	no	Hall
25	C₂×C₅	—	1891	2	no	—
26	C₂×C₅	—	1891	1	no	—
27	C₅	—	1891	1	no	Sylow
28	C₂²	—	61	1	no	Sylow
29	C₂	—	61	2	no	—
30	C₂	#34038658	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#34038658
commutator, cosocle, hypocenter	C₃₁×C₆₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃₁×C₆₁	C₂×C₅
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.