Finite Group Databasebeta

← C₂²×C₂₅×C₃₁₇ #44540148

Subgroups — C₂²×C₂₅×C₃₁₇ #44540148

Order 31700.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₅×C₃₁₇	C₂	1	3	yes	maximal, direct product factor
2	C₂₅×C₃₁₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅×C₃₁₇	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃₁₇	C₂×C₅	1	3	yes	—
5	C₅×C₃₁₇	C₂²×C₅	1	1	yes	characteristic
6	C₂²×C₃₁₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃₁₇	C₂×C₂₅	1	3	yes	direct product factor
8	C₃₁₇	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₂²×C₂₅	C₃₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₂₅	C₂×C₃₁₇	1	3	yes	direct product factor
11	C₂₅	C₂²×C₃₁₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₅	C₅×C₃₁₇	1	1	yes	characteristic
13	C₂×C₅	C₂×C₅×C₃₁₇	1	3	yes	—
14	C₅	C₂²×C₅×C₃₁₇	1	1	yes	characteristic
15	C₂²	C₂₅×C₃₁₇	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₂₅×C₃₁₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₃₁₇
socle, prime radical	C₂²×C₅×C₃₁₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₂₅×C₃₁₇	C₂	direct (N × H)
2. C₂₅×C₃₁₇	C₂²	direct (N × H)
6. C₂²×C₃₁₇	C₂₅	direct (N × H)
7. C₂×C₃₁₇	C₂×C₂₅	direct (N × H)
8. C₃₁₇	C₂²×C₂₅	direct (N × H)
9. C₂²×C₂₅	C₃₁₇	direct (N × H)
10. C₂×C₂₅	C₂×C₃₁₇	direct (N × H)
11. C₂₅	C₂²×C₃₁₇	direct (N × H)
15. C₂²	C₂₅×C₃₁₇	direct (N × H)
16. C₂	C₂×C₂₅×C₃₁₇	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₅×C₃₁₇	2
C₂²×C₅×C₃₁₇	5
C₂²×C₂₅	317