Subgroups — C₅×D₃×D₅₂₇ #44539360

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₅	D₃×D₅₂₇
commutator, cosocle, hypocenter	C₃×C₁₇×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₂²
LCS	G ▷ C₃×C₁₇×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₅₈₁	C₂	semidirect
2. C₅×D₃×C₁₇×C₃₁	C₂	semidirect
3. C₃×C₅×D₅₂₇	C₂	semidirect
5. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
6. D₃×D₅₂₇	C₅	direct (N × H)
8. C₅×D₅₂₇	D₃	direct (N × H)
10. D₁₅₈₁	C₂×C₅	semidirect
11. D₃×C₁₇×C₃₁	C₂×C₅	semidirect
12. C₃×D₅₂₇	C₂×C₅	semidirect
13. C₅×C₁₇×C₃₁	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₁	C₂²×C₅	semidirect
19. D₅₂₇	C₅×D₃	direct (N × H)
22. C₅×D₃×C₃₁	D₁₇	semidirect
25. C₁₇×C₃₁	C₂×C₅×D₃	semidirect
27. C₅×D₃×C₁₇	D₃₁	semidirect
29. C₃×C₅×C₃₁	C₂×D₁₇	semidirect
35. C₃×C₅×C₁₇	C₂×D₃₁	semidirect
39. D₃×C₃₁	C₅×D₁₇	semidirect
43. C₅×C₃₁	D₃×D₁₇	semidirect
47. D₃×C₁₇	C₅×D₃₁	semidirect
48. C₃×C₃₁	C₂×C₅×D₁₇	semidirect
49. C₅×C₁₇	D₃×D₃₁	semidirect
55. C₃×C₁₇	C₂×C₅×D₃₁	semidirect
59. C₃₁	C₅×D₃×D₁₇	semidirect
62. C₅×D₃	D₅₂₇	direct (N × H)
64. C₁₇	C₅×D₃×D₃₁	semidirect
65. C₃×C₅	C₂×D₅₂₇	semidirect
72. D₃	C₅×D₅₂₇	direct (N × H)
73. C₅	D₃×D₅₂₇	direct (N × H)
75. C₃	C₂×C₅×D₅₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₅₈₁	2
C₅×D₃×C₁₇×C₃₁	2
C₃×C₅×D₅₂₇	2
C₂×C₅×D₅₂₇	3
D₃×D₅₂₇	5
C₅×D₃×D₃₁	17
C₅×D₃×D₁₇	31

Subgroups — C5×D3×D527 #44539360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×D₅₂₇ #44539360