Subgroups — C₃×C₅×C₃₁×Dic₁₇ #44539249

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃₁×Dic₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₃₁×Dic₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic
7	C₅×C₁₇×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃₁×Dic₁₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₄×C₅×C₃₁	—	17	1	no	maximal, 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×C₅×Dic₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×C₃₁	D₁₇	1	1	yes	characteristic
14	C₄×C₅×C₃₁	—	17	1	no	Hall
15	C₁₇×C₃₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic
17	C₃×C₅×C₃₁	Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₄×C₃₁	—	17	1	no	Hall
19	C₅×Dic₁₇	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₃₁	C₃×D₁₇	1	1	yes	characteristic
21	C₃×C₅×C₁₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
22	C₃×Dic₁₇	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₃₁	C₅×D₁₇	1	1	yes	characteristic
24	C₂×C₅×C₁₇	C₂×C₃×C₃₁	1	1	yes	characteristic
25	C₅×C₃₁	C₃×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₄×C₃₁	—	17	1	no	Hall
27	C₂×C₃×C₁₇	C₂×C₅×C₃₁	1	1	yes	characteristic
28	C₃×C₃₁	C₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₇	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
30	Dic₁₇	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃₁	C₃×C₅×D₁₇	1	1	yes	characteristic
32	C₃×C₄×C₅	—	17	1	no	Hall
33	C₃×C₁₇	C₄×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₇	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
35	C₃₁	C₃×C₅×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃×C₅	C₃₁×D₁₇	1	1	yes	characteristic
37	C₄×C₅	—	17	1	no	Hall
38	C₁₇	C₃×C₄×C₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	C₃₁×Dic₁₇	1	1	yes	characteristic, direct product factor, Hall
40	C₃×C₄	—	17	1	no	Hall
41	C₂×C₅	C₃×C₃₁×D₁₇	1	1	yes	characteristic
42	C₂×C₃	C₅×C₃₁×D₁₇	1	1	yes	characteristic
43	C₅	C₃×C₃₁×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	—	17	1	no	Sylow
45	C₃	C₅×C₃₁×Dic₁₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₅×C₃₁×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₃₁	D₁₇
commutator, hypocenter	C₁₇	C₃×C₄×C₅×C₃₁
Frattini	C₂	C₃×C₅×C₃₁×D₁₇
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₇×C₃₁	C₂
cosocle	C₂×C₁₇	C₂×C₃×C₅×C₃₁
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₃×C₅×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₃₁×Dic₁₇	C₃	direct (N × H)
3. C₃×C₅×C₁₇×C₃₁	C₄	semidirect
4. C₃×C₃₁×Dic₁₇	C₅	direct (N × H)
7. C₅×C₁₇×C₃₁	C₃×C₄	semidirect
8. C₃₁×Dic₁₇	C₃×C₅	direct (N × H)
10. C₃×C₁₇×C₃₁	C₄×C₅	semidirect
12. C₃×C₅×Dic₁₇	C₃₁	direct (N × H)
15. C₁₇×C₃₁	C₃×C₄×C₅	semidirect
17. C₃×C₅×C₃₁	Dic₁₇	direct (N × H)
19. C₅×Dic₁₇	C₃×C₃₁	direct (N × H)
21. C₃×C₅×C₁₇	C₄×C₃₁	semidirect
22. C₃×Dic₁₇	C₅×C₃₁	direct (N × H)
25. C₅×C₃₁	C₃×Dic₁₇	direct (N × H)
28. C₃×C₃₁	C₅×Dic₁₇	direct (N × H)
29. C₅×C₁₇	C₃×C₄×C₃₁	semidirect
30. Dic₁₇	C₃×C₅×C₃₁	direct (N × H)
33. C₃×C₁₇	C₄×C₅×C₃₁	semidirect
35. C₃₁	C₃×C₅×Dic₁₇	direct (N × H)
38. C₁₇	C₃×C₄×C₅×C₃₁	semidirect
39. C₃×C₅	C₃₁×Dic₁₇	direct (N × H)
43. C₅	C₃×C₃₁×Dic₁₇	direct (N × H)
45. C₃	C₅×C₃₁×Dic₁₇	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×C₅×C₁₇×C₃₁	2
C₅×C₃₁×Dic₁₇	3
C₃×C₃₁×Dic₁₇	5
C₃×C₄×C₅×C₃₁	17
C₃×C₅×Dic₁₇	31

Subgroups — C3×C5×C31×Dic17 #44539249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₃₁×Dic₁₇ #44539249