Subgroups — D₅₁×D₃₁⋊C₅ #44539293

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	D₅₁×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₃₁⋊C₅	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	D₃₁×D₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₁₇⋊(D₃₁⋊C₅)	—	3	1	no	—
8	D₁₇×ΓL(1,𝔽₃₂)	—	3	1	no	—
9	C₁₇×D₃₁⋊C₅	D₃	1	1	yes	characteristic, complemented
10	D₁₅₈₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃₁×D₅₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₁₇×D₃₁	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	D₃×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	C₅×D₃	1	1	yes	characteristic, complemented
19	C₃₁×D₁₇	—	3	1	no	—
20	C₂×C₅×D₅₁	—	31	1	no	maximal, Hall
21	C₃⋊(D₃₁⋊C₅)	—	17	1	no	—
22	D₃×ΓL(1,𝔽₃₂)	—	17	1	no	—
23	C₃×D₃₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented
24	C₂×D₃₁⋊C₅	—	51	1	no	Hall
25	C₁₇×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₁₇	—	31	1	no	—
27	C₅×D₅₁	—	31	1	no	—
28	C₅×D₅₁	—	31	1	no	—
29	C₃×ΓL(1,𝔽₃₂)	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	D₃×D₃₁	—	17	1	no	Hall
31	C₂×C₅×D₁₇	—	93	1	no	Hall
32	C₂×ΓL(1,𝔽₃₂)	—	51	1	no	—
33	D₃₁⋊C₅	—	51	1	no	—
34	D₃₁⋊C₅	D₅₁	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₇	—	31	1	no	Hall
36	C₂×D₅₁	—	31	1	no	Hall
37	D₉₃	—	17	1	no	—
38	C₃×D₃₁	C₅×D₁₇	1	1	yes	characteristic, complemented
39	D₃×C₃₁	—	17	1	no	—
40	C₂×C₅×C₁₇	—	31	1	no	—
41	C₅×D₁₇	—	93	1	no	—
42	C₅×D₁₇	—	93	1	no	—
43	ΓL(1,𝔽₃₂)	C₂×D₅₁	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	51	1	no	Hall
45	C₂×C₃×C₁₇	—	31	1	no	—
46	D₅₁	—	31	1	no	—
47	D₅₁	D₃₁⋊C₅	1	1	yes	characteristic, direct product factor
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	—	51	1	no	—
52	D₃₁	—	51	1	no	—
53	D₃₁	C₅×D₅₁	1	1	yes	characteristic, complemented
54	C₂×C₅×D₃	—	527	1	no	Hall
55	C₃×C₁₇	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₇	—	31	1	no	—
57	D₁₇	—	3	1	no	—
58	D₁₇	—	93	1	no	—
59	C₃₁	C₂×C₅×D₅₁	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃×C₅	—	31	1	no	—
61	C₅×D₃	—	527	1	no	—
62	C₅×D₃	—	527	1	no	—
63	C₂²×C₅	—	1581	1	no	Hall
64	C₁₇	D₃×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	—	31	1	no	—
68	C₂×C₅	—	1581	1	no	—
69	C₂×C₅	—	1581	1	no	—
70	C₂×C₃	—	31	1	no	—
71	D₃	—	527	1	no	—
72	D₃	—	17	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	—	31	1	no	—
77	C₂	—	1581	1	no	—
78	C₂	—	51	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. D₅₁×ΓL(1,𝔽₃₂)	C₂	semidirect
3. C₃×C₁₇×D₃₁⋊C₅	C₂	semidirect
5. C₃×C₁₇×ΓL(1,𝔽₃₂)	C₂²	semidirect
6. D₃₁×D₅₁	C₅	semidirect
9. C₁₇×D₃₁⋊C₅	D₃	semidirect
10. D₁₅₈₁	C₂×C₅	semidirect
11. C₃₁×D₅₁	C₂×C₅	semidirect
12. C₃×C₁₇×D₃₁	C₂×C₅	semidirect
13. C₁₇×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₁	C₂²×C₅	semidirect
18. C₁₇×D₃₁	C₅×D₃	semidirect
23. C₃×D₃₁⋊C₅	D₁₇	semidirect
25. C₁₇×C₃₁	C₂×C₅×D₃	semidirect
29. C₃×ΓL(1,𝔽₃₂)	C₂×D₁₇	semidirect
34. D₃₁⋊C₅	D₅₁	direct (N × H)
38. C₃×D₃₁	C₅×D₁₇	semidirect
43. ΓL(1,𝔽₃₂)	C₂×D₅₁	semidirect
47. D₅₁	D₃₁⋊C₅	direct (N × H)
48. C₃×C₃₁	C₂×C₅×D₁₇	semidirect
53. D₃₁	C₅×D₅₁	semidirect
55. C₃×C₁₇	C₂×D₃₁⋊C₅	semidirect
59. C₃₁	C₂×C₅×D₅₁	semidirect
64. C₁₇	D₃×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
D₅₁×ΓL(1,𝔽₃₂)	2
C₃×C₁₇×D₃₁⋊C₅	2
D₁₇×D₃₁⋊C₅	3
D₃₁×D₅₁	5
D₃×D₃₁⋊C₅	17
C₂×C₅×D₅₁	31

Subgroups — D51×D31⋊C5 #44539293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₁×D₃₁⋊C₅ #44539293