Subgroups — C₂×C₁₇×AGL(1,𝔽₃₁) #44539284

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×AGL(1,𝔽₃₁)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×(C₃₁⋊C₃)⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₇×(C₃₁⋊C₃)⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇×D₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₇×D₃₁⋊C₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₇×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₇×D₃₁⋊C₃	C₂×C₅	1	2	yes	complemented
9	C₂×C₁₇×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
10	C₁₇×ΓL(1,𝔽₃₂)	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₇×D₃₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×AGL(1,𝔽₃₁)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₇×C₃₁⋊C₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
15	C₁₇×D₃₁	C₂×C₃×C₅	1	2	yes	complemented
16	C₂²×C₃×C₅×C₁₇	—	31	1	no	maximal, Hall
17	C₂×(C₃₁⋊C₃)⋊C₅	C₂×C₁₇	1	1	yes	characteristic, complemented
18	AGL(1,𝔽₃₁)	C₂×C₁₇	1	2	yes	direct product factor
19	C₂×D₃₁⋊C₅	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₁₇×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₁₇	—	31	1	no	—
22	C₂×C₃×C₅×C₁₇	—	31	2	no	—
23	(C₃₁⋊C₃)⋊C₅	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₃₁⋊C₃	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₅×C₁₇	—	31	1	no	Hall
26	C₂×ΓL(1,𝔽₃₂)	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
27	D₃₁⋊C₅	C₂×C₃×C₁₇	1	2	yes	complemented
28	C₃×C₅×C₁₇	—	31	1	no	Hall
29	C₂²×C₃×C₁₇	—	31	1	no	Hall
30	C₂×C₃₁⋊C₃	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
31	D₃₁⋊C₃	C₂×C₅×C₁₇	1	2	yes	complemented
32	C₂×C₅×C₁₇	—	31	2	no	—
33	C₂×C₅×C₁₇	—	31	1	no	—
34	ΓL(1,𝔽₃₂)	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃₁	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₇	—	31	2	no	—
37	C₂×C₃×C₁₇	—	31	1	no	—
38	C₃₁⋊C₃	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	—	31	1	no	Hall
40	C₂²×C₁₇	—	31	1	no	Hall
41	C₂×C₃₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
42	D₃₁	C₂×C₃×C₅×C₁₇	1	2	yes	complemented
43	C₂²×C₃×C₅	—	31	1	no	Hall
44	C₃×C₁₇	—	31	1	no	Hall
45	C₂×C₁₇	—	31	2	no	—
46	C₂×C₁₇	AGL(1,𝔽₃₁)	1	1	yes	characteristic, direct product factor
47	C₃₁	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	31	2	no	—
49	C₂×C₃×C₅	—	31	1	no	—
50	C₂²×C₅	—	31	1	no	Hall
51	C₁₇	C₂×AGL(1,𝔽₃₁)	1	1	yes	characteristic, direct product factor, Sylow
52	C₃×C₅	—	31	1	no	Hall
53	C₂²×C₃	—	31	1	no	Hall
54	C₂×C₅	—	31	2	no	—
55	C₂×C₅	—	31	1	no	—
56	C₂×C₃	—	31	2	no	—
57	C₂×C₃	—	31	1	no	—
58	C₅	—	31	1	no	Sylow
59	C₂²	—	31	1	no	Sylow
60	C₃	—	31	1	no	Sylow
61	C₂	—	31	2	no	—
62	C₂	C₁₇×AGL(1,𝔽₃₁)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	AGL(1,𝔽₃₁)
commutator, cosocle, hypocenter	C₃₁	C₂²×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₃₁	C₂×C₃×C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×AGL(1,𝔽₃₁)	C₂	direct (N × H)
2. C₂×C₁₇×(C₃₁⋊C₃)⋊C₅	C₂	semidirect
3. C₂×C₁₇×D₃₁⋊C₅	C₃	semidirect
4. C₁₇×(C₃₁⋊C₃)⋊C₅	C₂²	semidirect
5. C₂×C₁₇×D₃₁⋊C₃	C₅	semidirect
6. C₁₇×D₃₁⋊C₅	C₂×C₃	semidirect
7. C₂×C₁₇×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
8. C₁₇×D₃₁⋊C₃	C₂×C₅	semidirect
9. C₂×C₁₇×C₃₁⋊C₃	C₂×C₅	semidirect
10. C₁₇×ΓL(1,𝔽₃₂)	C₂²×C₃	semidirect
11. C₂×C₁₇×D₃₁	C₃×C₅	semidirect
12. C₂×AGL(1,𝔽₃₁)	C₁₇	direct (N × H)
13. C₁₇×C₃₁⋊C₃	C₂²×C₅	semidirect
14. C₂×C₁₇×C₃₁	C₂×C₃×C₅	semidirect
15. C₁₇×D₃₁	C₂×C₃×C₅	semidirect
17. C₂×(C₃₁⋊C₃)⋊C₅	C₂×C₁₇	semidirect
18. AGL(1,𝔽₃₁)	C₂×C₁₇	direct (N × H)
19. C₂×D₃₁⋊C₅	C₃×C₁₇	semidirect
20. C₁₇×C₃₁	C₂²×C₃×C₅	semidirect
23. (C₃₁⋊C₃)⋊C₅	C₂²×C₁₇	semidirect
24. C₂×D₃₁⋊C₃	C₅×C₁₇	semidirect
26. C₂×ΓL(1,𝔽₃₂)	C₂×C₃×C₁₇	semidirect
27. D₃₁⋊C₅	C₂×C₃×C₁₇	semidirect
30. C₂×C₃₁⋊C₃	C₂×C₅×C₁₇	semidirect
31. D₃₁⋊C₃	C₂×C₅×C₁₇	semidirect
34. ΓL(1,𝔽₃₂)	C₂²×C₃×C₁₇	semidirect
35. C₂×D₃₁	C₃×C₅×C₁₇	semidirect
38. C₃₁⋊C₃	C₂²×C₅×C₁₇	semidirect
41. C₂×C₃₁	C₂×C₃×C₅×C₁₇	semidirect
42. D₃₁	C₂×C₃×C₅×C₁₇	semidirect
46. C₂×C₁₇	AGL(1,𝔽₃₁)	direct (N × H)
47. C₃₁	C₂²×C₃×C₅×C₁₇	semidirect
51. C₁₇	C₂×AGL(1,𝔽₃₁)	direct (N × H)
62. C₂	C₁₇×AGL(1,𝔽₃₁)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×AGL(1,𝔽₃₁)	2
C₂×C₁₇×(C₃₁⋊C₃)⋊C₅	2
C₂×C₁₇×D₃₁⋊C₅	3
C₂×C₁₇×D₃₁⋊C₃	5
C₂×AGL(1,𝔽₃₁)	17
C₂²×C₃×C₅×C₁₇	31

Subgroups — C2×C17×AGL(1,𝔽31) #44539284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×AGL(1,𝔽₃₁) #44539284