Subgroups — C₅×A₄×C₁₇×C₃₁ #44539394

Order 31620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₁₇×C₃₁	—	4	1	no	maximal, Hall
3	A₄×C₁₇×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₁₇×C₃₁	—	3	1	no	—
5	C₅×C₁₇×C₃₁	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₁₇×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×A₄×C₃₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₇×C₃₁	—	4	1	no	Hall
9	C₂×C₁₇×C₃₁	—	3	1	no	—
10	C₅×A₄×C₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₅×C₃₁	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₁₇×C₃₁	C₅×A₄	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₃₁	—	4	1	no	Hall
14	A₄×C₃₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂²×C₅×C₁₇	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₃₁	—	3	1	no	—
17	C₃×C₅×C₁₇	—	4	1	no	Hall
18	A₄×C₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅×C₁₇	—	3	1	no	—
20	C₅×C₃₁	A₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₃₁	—	4	1	no	Hall
23	C₅×C₁₇	A₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
24	C₂²×C₁₇	C₃×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃₁	—	3	1	no	—
26	C₅×A₄	C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₁₇	—	4	1	no	Hall
28	C₂×C₁₇	—	3	1	no	—
29	C₃₁	C₅×A₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²×C₅	C₃×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Hall
31	C₁₇	C₅×A₄×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₅	—	4	1	no	Hall
33	A₄	C₅×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₅	—	3	1	no	—
35	C₅	A₄×C₁₇×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²	C₃×C₅×C₁₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	4	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₇×C₃₁	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₁₇×C₃₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₇×C₃₁	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₁₇×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₇×C₃₁	C₃	semidirect
3. A₄×C₁₇×C₃₁	C₅	direct (N × H)
5. C₅×C₁₇×C₃₁	A₄	direct (N × H)
6. C₂²×C₁₇×C₃₁	C₃×C₅	semidirect
7. C₅×A₄×C₃₁	C₁₇	direct (N × H)
10. C₅×A₄×C₁₇	C₃₁	direct (N × H)
11. C₂²×C₅×C₃₁	C₃×C₁₇	semidirect
12. C₁₇×C₃₁	C₅×A₄	direct (N × H)
14. A₄×C₃₁	C₅×C₁₇	direct (N × H)
15. C₂²×C₅×C₁₇	C₃×C₃₁	semidirect
18. A₄×C₁₇	C₅×C₃₁	direct (N × H)
20. C₅×C₃₁	A₄×C₁₇	direct (N × H)
21. C₂²×C₃₁	C₃×C₅×C₁₇	semidirect
23. C₅×C₁₇	A₄×C₃₁	direct (N × H)
24. C₂²×C₁₇	C₃×C₅×C₃₁	semidirect
26. C₅×A₄	C₁₇×C₃₁	direct (N × H)
29. C₃₁	C₅×A₄×C₁₇	direct (N × H)
30. C₂²×C₅	C₃×C₁₇×C₃₁	semidirect
31. C₁₇	C₅×A₄×C₃₁	direct (N × H)
33. A₄	C₅×C₁₇×C₃₁	direct (N × H)
35. C₅	A₄×C₁₇×C₃₁	direct (N × H)
36. C₂²	C₃×C₅×C₁₇×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₇×C₃₁	3
C₃×C₅×C₁₇×C₃₁	4
A₄×C₁₇×C₃₁	5
C₅×A₄×C₃₁	17
C₅×A₄×C₁₇	31

Subgroups — C5×A4×C17×C31 #44539394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×A₄×C₁₇×C₃₁ #44539394