Subgroups — C₅×#17986945 #37503513

Order 22785.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₁×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#17986945	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×#10620252	—	7	1	no	maximal
4	C₃₁×C₄₉	C₃×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₃₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	C₅×C₄₉⋊C₃	—	31	1	no	maximal, Hall
7	#10620252	—	7	1	no	—
8	C₅×C₃₁⋊C₃	—	49	1	no	Hall
9	C₅×C₄₉	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
10	C₇×C₃₁	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₅×C₃₁	C₄₉⋊C₃	1	1	yes	characteristic, complemented, Hall
12	C₄₉⋊C₃	—	31	1	no	Hall
13	C₅×ΓL(1,𝔽₈)	—	217	1	no	—
14	C₃₁⋊C₃	—	49	1	no	Hall
15	C₄₉	C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₅×C₇	#10620252	1	1	yes	characteristic
17	C₃₁	C₅×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	ΓL(1,𝔽₈)	—	217	1	no	—
19	C₃×C₅	—	1519	1	no	Hall
20	C₇	C₅×#10620252	1	1	yes	characteristic
21	C₅	#17986945	1	1	yes	characteristic, direct product factor, Sylow
22	C₃	—	1519	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	#17986945
commutator, cosocle, hypocenter	C₃₁×C₄₉	C₃×C₅
Frattini	C₇	C₅×#10620252
Fitting	C₅×C₃₁×C₄₉	C₃
socle	C₅×C₇×C₃₁	ΓL(1,𝔽₈)
LCS	G ▷ C₃₁×C₄₉
UCS	C₁ ◁ C₅

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.