Subgroups — C₂×C₁₇×C₂₅×C₃₇ #44537782

Order 31450.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₂₅×C₃₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₇×C₃₇	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic
4	C₂×C₂₅×C₃₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₇×C₃₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂₅×C₃₇	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₇×C₂₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₃₇	C₂×C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₁₇×C₂₅	C₂×C₃₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₃₇	C₅×C₁₇	1	1	yes	characteristic
11	C₅×C₃₇	C₂×C₅×C₁₇	1	1	yes	characteristic
12	C₂×C₅×C₁₇	C₅×C₃₇	1	1	yes	characteristic
13	C₅×C₁₇	C₂×C₅×C₃₇	1	1	yes	characteristic
14	C₂×C₃₇	C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₂₅	C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃₇	C₂×C₁₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₁₇	C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₂₅	C₂×C₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₁₇	C₂×C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₅	C₅×C₁₇×C₃₇	1	1	yes	characteristic
21	C₅	C₂×C₅×C₁₇×C₃₇	1	1	yes	characteristic
22	C₂	C₁₇×C₂₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂×C₅×C₁₇×C₃₇
socle, prime radical	C₂×C₅×C₁₇×C₃₇	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₂₅×C₃₇	C₂	direct (N × H)
4. C₂×C₂₅×C₃₇	C₁₇	direct (N × H)
5. C₂×C₁₇×C₃₇	C₂₅	direct (N × H)
6. C₂₅×C₃₇	C₂×C₁₇	direct (N × H)
7. C₂×C₁₇×C₂₅	C₃₇	direct (N × H)
8. C₁₇×C₃₇	C₂×C₂₅	direct (N × H)
9. C₁₇×C₂₅	C₂×C₃₇	direct (N × H)
14. C₂×C₃₇	C₁₇×C₂₅	direct (N × H)
15. C₂×C₂₅	C₁₇×C₃₇	direct (N × H)
16. C₃₇	C₂×C₁₇×C₂₅	direct (N × H)
17. C₂×C₁₇	C₂₅×C₃₇	direct (N × H)
18. C₂₅	C₂×C₁₇×C₃₇	direct (N × H)
19. C₁₇	C₂×C₂₅×C₃₇	direct (N × H)
22. C₂	C₁₇×C₂₅×C₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×C₂₅×C₃₇	2
C₂×C₅×C₁₇×C₃₇	5
C₂×C₂₅×C₃₇	17
C₂×C₁₇×C₂₅	37

Subgroups — C2×C17×C25×C37 #44537782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₂₅×C₃₇ #44537782