Subgroups — #49180647

Order 37820.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₆₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₆₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₈₉₁	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	Dic₆₁⋊C₅	—	31	1	no	maximal, Hall
7	C₅×Dic₃₁	—	61	1	no	maximal, Hall
8	C₂×C₆₁⋊C₅	D₃₁	1	1	yes	characteristic
9	C₂×C₅×C₃₁	—	61	1	no	—
10	C₆₁⋊C₅	Dic₃₁	1	1	yes	characteristic, complemented, Hall
11	Dic₆₁	—	31	1	no	Hall
12	C₅×C₃₁	—	61	1	no	Hall
13	Dic₃₁	—	61	1	no	Hall
14	C₂×C₆₁	C₅×D₃₁	1	1	yes	characteristic
15	C₂×C₃₁	D₆₁⋊C₅	1	1	yes	characteristic
16	C₆₁	C₅×Dic₃₁	1	1	yes	characteristic, complemented, Sylow
17	C₃₁	Dic₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₅	—	1891	1	no	Hall
19	C₂×C₅	—	61	1	no	—
20	C₅	—	61	1	no	Sylow
21	C₄	—	1891	1	no	Sylow
22	C₂	(C₆₁⋊C₅)⋊D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₆₁⋊C₅)⋊D₃₁
commutator, hypocenter	C₃₁×C₆₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₃₁×C₆₁	C₂×C₅
prime radical	C₂×C₃₁×C₆₁⋊C₅	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.