Subgroups — D₁₇×C₃⋊(D₃₁⋊C₅) #44539294

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₁₇⋊(D₃₁⋊C₅))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₃⋊(D₃₁⋊C₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₇×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₃₁⋊C₅	—	3	1	no	maximal, Hall
5	C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×D₉₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₁₇⋊(D₃₁⋊C₅)	—	3	1	no	—
8	D₁₇×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic, complemented
9	C₁₇×D₃₁⋊C₅	—	3	1	no	—
10	D₁₅₈₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₁₇×D₉₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₃₁×D₁₇	C₂×C₅	1	1	yes	characteristic, complemented
13	C₁₇×ΓL(1,𝔽₃₂)	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₃₁	—	3	1	no	Hall
15	C₂×C₃⋊(D₃₁⋊C₅)	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	D₅₂₇	—	3	1	no	—
18	C₁₇×D₃₁	—	3	1	no	—
19	C₃₁×D₁₇	C₅×D₃	1	1	yes	characteristic, complemented
20	C₅×D₃×D₁₇	—	31	1	no	maximal, Hall
21	C₂×C₃×ΓL(1,𝔽₃₂)	—	17	1	no	—
22	C₃⋊(D₃₁⋊C₅)	—	17	1	no	—
23	C₃⋊(D₃₁⋊C₅)	D₁₇	1	1	yes	characteristic, direct product factor
24	C₂×D₃₁⋊C₅	—	51	1	no	Hall
25	C₁₇×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
26	C₅×D₅₁	—	31	1	no	—
27	C₅×D₃×C₁₇	—	31	1	no	—
28	C₃×C₅×D₁₇	—	31	1	no	—
29	C₃×ΓL(1,𝔽₃₂)	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₉₃	—	17	1	no	Hall
31	C₂×C₅×D₁₇	—	93	1	no	Hall
32	C₂×ΓL(1,𝔽₃₂)	—	17	1	no	—
33	D₃₁⋊C₅	—	3	1	no	—
34	D₃₁⋊C₅	—	51	1	no	—
35	C₃×C₅×C₁₇	—	31	1	no	Hall
36	D₃×D₁₇	—	31	1	no	Hall
37	C₂×C₃×C₃₁	—	17	1	no	—
38	D₉₃	—	17	1	no	—
39	D₉₃	C₅×D₁₇	1	1	yes	characteristic, complemented
40	C₂×C₅×C₁₇	—	93	1	no	—
41	C₅×D₁₇	—	31	1	no	—
42	C₅×D₁₇	—	93	1	no	—
43	ΓL(1,𝔽₃₂)	D₃×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	51	1	no	Hall
45	D₅₁	—	31	1	no	—
46	C₃×D₁₇	D₃₁⋊C₅	1	1	yes	characteristic, complemented
47	D₃×C₁₇	—	31	1	no	—
48	C₃×C₃₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	—	31	1	no	Hall
50	C₂×D₁₇	—	93	1	no	Hall
51	C₂×C₃₁	—	17	1	no	—
52	D₃₁	—	3	1	no	—
53	D₃₁	—	51	1	no	—
54	C₂×C₅×D₃	—	527	1	no	Hall
55	C₃×C₁₇	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₇	—	93	1	no	—
57	D₁₇	—	93	1	no	—
58	D₁₇	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
59	C₃₁	C₅×D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃×C₅	—	527	1	no	—
61	C₅×D₃	—	527	1	no	—
62	C₅×D₃	—	31	1	no	—
63	C₂²×C₅	—	1581	1	no	Hall
64	C₁₇	C₂×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	31	1	no	Hall
66	C₂×D₃	—	527	1	no	Hall
67	C₂×C₅	—	527	1	no	—
68	C₂×C₅	—	1581	1	no	—
69	C₂×C₅	—	93	1	no	—
70	C₂×C₃	—	17	1	no	—
71	D₃	—	527	1	no	—
72	D₃	—	31	1	no	—
73	C₅	—	31	1	no	Sylow
74	C₂²	—	1581	1	no	Sylow
75	C₃	D₁₇×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	17	1	no	—
77	C₂	—	1581	1	no	—
78	C₂	—	93	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₁₇⋊(D₃₁⋊C₅))	C₂	semidirect
2. C₁₇×C₃⋊(D₃₁⋊C₅)	C₂	semidirect
3. C₃×D₁₇×ΓL(1,𝔽₃₂)	C₂	semidirect
5. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂²	semidirect
6. D₁₇×D₉₃	C₅	semidirect
8. D₁₇×ΓL(1,𝔽₃₂)	D₃	semidirect
10. D₁₅₈₁	C₂×C₅	semidirect
11. C₁₇×D₉₃	C₂×C₅	semidirect
12. C₃×C₃₁×D₁₇	C₂×C₅	semidirect
13. C₁₇×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₁	C₂²×C₅	semidirect
19. C₃₁×D₁₇	C₅×D₃	semidirect
23. C₃⋊(D₃₁⋊C₅)	D₁₇	direct (N × H)
25. C₁₇×C₃₁	C₂×C₅×D₃	semidirect
29. C₃×ΓL(1,𝔽₃₂)	C₂×D₁₇	semidirect
39. D₉₃	C₅×D₁₇	semidirect
43. ΓL(1,𝔽₃₂)	D₃×D₁₇	semidirect
46. C₃×D₁₇	D₃₁⋊C₅	semidirect
48. C₃×C₃₁	C₂×C₅×D₁₇	semidirect
55. C₃×C₁₇	C₂×D₃₁⋊C₅	semidirect
58. D₁₇	C₃⋊(D₃₁⋊C₅)	direct (N × H)
59. C₃₁	C₅×D₃×D₁₇	semidirect
64. C₁₇	C₂×C₃⋊(D₃₁⋊C₅)	semidirect
75. C₃	D₁₇×D₃₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₁₇⋊(D₃₁⋊C₅))	2
C₁₇×C₃⋊(D₃₁⋊C₅)	2
C₃×D₁₇×ΓL(1,𝔽₃₂)	2
D₁₇×D₃₁⋊C₅	3
D₁₇×D₉₃	5
C₂×C₃⋊(D₃₁⋊C₅)	17
C₅×D₃×D₁₇	31

Subgroups — D17×C3⋊(D31⋊C5) #44539294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×C₃⋊(D₃₁⋊C₅) #44539294