Subgroups — C₃×C₁₇×Dic₃₁⋊C₅ #44539263

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₇×Dic₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×Dic₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₇×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₁₇×ΓL(1,𝔽₃₂)	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₇×Dic₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×Dic₃₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₇×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
12	C₃×C₄×C₅×C₁₇	—	31	1	no	maximal, Hall
13	C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₁₇	1	1	yes	characteristic
14	Dic₃₁⋊C₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₁₇×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₇	—	31	1	no	—
17	C₃×ΓL(1,𝔽₃₂)	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₃×Dic₃₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₄×C₅×C₁₇	—	31	1	no	Hall
20	C₂×ΓL(1,𝔽₃₂)	C₂×C₃×C₁₇	1	1	yes	characteristic
21	C₃×C₅×C₁₇	—	31	1	no	Hall
22	C₃×C₄×C₁₇	—	31	1	no	Hall
23	C₂×C₃×C₃₁	C₂×C₅×C₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	—	31	1	no	—
25	ΓL(1,𝔽₃₂)	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
26	Dic₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₇	D₃₁⋊C₅	1	1	yes	characteristic
28	C₃×C₃₁	C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
29	C₅×C₁₇	—	31	1	no	Hall
30	C₄×C₁₇	—	31	1	no	Hall
31	C₂×C₃₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
32	C₃×C₄×C₅	—	31	1	no	Hall
33	C₃×C₁₇	Dic₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₇	C₃×D₃₁⋊C₅	1	1	yes	characteristic
35	C₃₁	C₃×C₄×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₅	—	31	1	no	—
37	C₄×C₅	—	31	1	no	Hall
38	C₁₇	C₃×Dic₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	—	31	1	no	Hall
40	C₃×C₄	—	31	1	no	Hall
41	C₂×C₅	—	31	1	no	—
42	C₂×C₃	C₁₇×D₃₁⋊C₅	1	1	yes	characteristic
43	C₅	—	31	1	no	Sylow
44	C₄	—	31	1	no	Sylow
45	C₃	C₁₇×Dic₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₁₇×D₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₃₁⋊C₅
commutator, hypocenter	C₃₁	C₃×C₄×C₅×C₁₇
Frattini	C₂	C₃×C₁₇×D₃₁⋊C₅
Fitting, socle	C₂×C₃×C₁₇×C₃₁	C₂×C₅
prime radical	C₂×C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂
cosocle	C₂×C₃₁	C₂×C₃×C₅×C₁₇
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×Dic₃₁⋊C₅	C₃	direct (N × H)
3. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₄	semidirect
4. C₃×C₁₇×Dic₃₁	C₅	semidirect
7. C₁₇×ΓL(1,𝔽₃₂)	C₃×C₄	semidirect
8. C₁₇×Dic₃₁	C₃×C₅	semidirect
9. C₃×Dic₃₁⋊C₅	C₁₇	direct (N × H)
10. C₃×C₁₇×C₃₁	C₄×C₅	semidirect
14. Dic₃₁⋊C₅	C₃×C₁₇	direct (N × H)
15. C₁₇×C₃₁	C₃×C₄×C₅	semidirect
17. C₃×ΓL(1,𝔽₃₂)	C₄×C₁₇	semidirect
18. C₃×Dic₃₁	C₅×C₁₇	semidirect
25. ΓL(1,𝔽₃₂)	C₃×C₄×C₁₇	semidirect
26. Dic₃₁	C₃×C₅×C₁₇	semidirect
28. C₃×C₃₁	C₄×C₅×C₁₇	semidirect
33. C₃×C₁₇	Dic₃₁⋊C₅	direct (N × H)
35. C₃₁	C₃×C₄×C₅×C₁₇	semidirect
38. C₁₇	C₃×Dic₃₁⋊C₅	direct (N × H)
45. C₃	C₁₇×Dic₃₁⋊C₅	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×C₃×C₁₇×ΓL(1,𝔽₃₂)	2
C₁₇×Dic₃₁⋊C₅	3
C₃×C₁₇×Dic₃₁	5
C₃×Dic₃₁⋊C₅	17
C₃×C₄×C₅×C₁₇	31

Subgroups — C3×C17×Dic31⋊C5 #44539263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×Dic₃₁⋊C₅ #44539263