Subgroups — C₂²×C₅×C₁₇×C₃₁⋊C₃ #44539396

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂²×C₅×C₁₇×C₃₁	C₃	semidirect
3. C₅×C₁₇×C₃₁⋊C₃	C₂²	direct (N × H)
4. C₂²×C₁₇×C₃₁⋊C₃	C₅	direct (N × H)
5. C₂×C₅×C₁₇×C₃₁	C₂×C₃	semidirect
6. C₂×C₁₇×C₃₁⋊C₃	C₂×C₅	direct (N × H)
7. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
8. C₂²×C₁₇×C₃₁	C₃×C₅	semidirect
9. C₂²×C₅×C₃₁⋊C₃	C₁₇	direct (N × H)
10. C₁₇×C₃₁⋊C₃	C₂²×C₅	direct (N × H)
11. C₂×C₁₇×C₃₁	C₂×C₃×C₅	semidirect
13. C₂×C₅×C₃₁⋊C₃	C₂×C₁₇	direct (N × H)
14. C₂²×C₅×C₃₁	C₃×C₁₇	semidirect
15. C₁₇×C₃₁	C₂²×C₃×C₅	semidirect
17. C₅×C₃₁⋊C₃	C₂²×C₁₇	direct (N × H)
18. C₂²×C₃₁⋊C₃	C₅×C₁₇	direct (N × H)
19. C₂²×C₅×C₁₇	C₃₁⋊C₃	direct (N × H)
20. C₂×C₅×C₃₁	C₂×C₃×C₁₇	semidirect
23. C₂×C₃₁⋊C₃	C₂×C₅×C₁₇	direct (N × H)
24. C₂×C₅×C₁₇	C₂×C₃₁⋊C₃	direct (N × H)
25. C₅×C₃₁	C₂²×C₃×C₁₇	semidirect
26. C₂²×C₃₁	C₃×C₅×C₁₇	semidirect
28. C₃₁⋊C₃	C₂²×C₅×C₁₇	direct (N × H)
29. C₅×C₁₇	C₂²×C₃₁⋊C₃	direct (N × H)
30. C₂²×C₁₇	C₅×C₃₁⋊C₃	direct (N × H)
31. C₂×C₃₁	C₂×C₃×C₅×C₁₇	semidirect
34. C₂×C₁₇	C₂×C₅×C₃₁⋊C₃	direct (N × H)
35. C₃₁	C₂²×C₃×C₅×C₁₇	semidirect
37. C₂²×C₅	C₁₇×C₃₁⋊C₃	direct (N × H)
38. C₁₇	C₂²×C₅×C₃₁⋊C₃	direct (N × H)
41. C₂×C₅	C₂×C₁₇×C₃₁⋊C₃	direct (N × H)
43. C₅	C₂²×C₁₇×C₃₁⋊C₃	direct (N × H)
44. C₂²	C₅×C₁₇×C₃₁⋊C₃	direct (N × H)
46. C₂	C₂×C₅×C₁₇×C₃₁⋊C₃	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×C₅×C₁₇×C₃₁⋊C₃	2
C₂²×C₅×C₁₇×C₃₁	3
C₂²×C₁₇×C₃₁⋊C₃	5
C₂²×C₅×C₃₁⋊C₃	17
C₂²×C₃×C₅×C₁₇	31

Subgroups — C22×C5×C17×C31⋊C3 #44539396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₁₇×C₃₁⋊C₃ #44539396