Subgroups — C₄×C₅×C₁₇×C₃₁ #24902011

Order 10540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₃₁	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₄×C₅×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₃₁	C₂×C₁₇	1	1	yes	characteristic
9	C₂×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic
10	C₅×C₃₁	C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₄×C₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₅×C₁₇	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic
15	C₂×C₁₇	C₂×C₅×C₃₁	1	1	yes	characteristic
16	C₃₁	C₄×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₄×C₅	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₇	C₄×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	C₂×C₁₇×C₃₁	1	1	yes	characteristic
20	C₅	C₄×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₅×C₁₇×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅×C₁₇×C₃₁
socle, prime radical	C₂×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₇×C₃₁	C₄	direct (N × H)
3. C₄×C₁₇×C₃₁	C₅	direct (N × H)
5. C₄×C₅×C₃₁	C₁₇	direct (N × H)
6. C₁₇×C₃₁	C₄×C₅	direct (N × H)
7. C₄×C₅×C₁₇	C₃₁	direct (N × H)
10. C₅×C₃₁	C₄×C₁₇	direct (N × H)
11. C₄×C₃₁	C₅×C₁₇	direct (N × H)
12. C₅×C₁₇	C₄×C₃₁	direct (N × H)
13. C₄×C₁₇	C₅×C₃₁	direct (N × H)
16. C₃₁	C₄×C₅×C₁₇	direct (N × H)
17. C₄×C₅	C₁₇×C₃₁	direct (N × H)
18. C₁₇	C₄×C₅×C₃₁	direct (N × H)
20. C₅	C₄×C₁₇×C₃₁	direct (N × H)
21. C₄	C₅×C₁₇×C₃₁	direct (N × H)

Subgroups — C4×C5×C17×C31 #24902011

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₅×C₁₇×C₃₁ #24902011