Subgroups — C₅×D₁₇×D₁₁₁ #49179857

Order 37740.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₈₈₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₇×D₁₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₇×D₃₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×D₁₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₆₂₉	—	3	1	no	—
8	C₅×D₁₇×C₃₇	D₃	1	1	yes	characteristic, complemented
9	C₅×C₁₇×D₃₇	—	3	1	no	—
10	D₁₈₈₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₁₇×D₁₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×C₁₇×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₃₇	—	3	1	no	Hall
15	C₂×C₅×D₁₁₁	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₃₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	D₆₂₉	—	3	1	no	—
18	C₁₇×D₃₇	—	3	1	no	—
19	D₁₇×C₃₇	C₅×D₃	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×C₃₇	—	17	1	no	—
21	C₅×D₁₁₁	—	17	1	no	—
22	C₅×D₁₁₁	D₁₇	1	1	yes	characteristic, direct product factor
23	C₅×D₃×D₁₇	—	37	1	no	maximal, Hall
24	C₂×C₅×D₃₇	—	51	1	no	Hall
25	C₁₇×C₃₇	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅×C₃₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
27	C₅×D₅₁	—	37	1	no	—
28	C₅×D₃×C₁₇	—	37	1	no	—
29	C₃×C₅×D₁₇	D₃₇	1	1	yes	characteristic, complemented
30	C₂×D₁₁₁	—	17	1	no	Hall
31	C₂×C₅×C₃₇	—	17	1	no	—
32	C₅×D₃₇	—	3	1	no	—
33	C₅×D₃₇	—	51	1	no	—
34	C₂×C₅×D₁₇	—	111	1	no	Hall
35	C₃×C₅×C₁₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₃₇	—	17	1	no	—
37	D₁₁₁	—	17	1	no	—
38	D₁₁₁	C₅×D₁₇	1	1	yes	characteristic, direct product factor
39	D₃×D₁₇	—	37	1	no	Hall
40	C₅×C₃₇	D₃×D₁₇	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₁₇	—	111	1	no	—
42	C₅×D₁₇	—	111	1	no	—
43	C₅×D₁₇	D₁₁₁	1	1	yes	characteristic, direct product factor
44	C₂×D₃₇	—	51	1	no	Hall
45	C₃×C₃₇	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
46	D₅₁	—	37	1	no	—
47	C₃×D₁₇	C₅×D₃₇	1	1	yes	characteristic, complemented
48	D₃×C₁₇	—	37	1	no	—
49	C₅×C₁₇	C₂×D₁₁₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃₇	—	17	1	no	—
51	D₃₇	—	3	1	no	—
52	D₃₇	—	51	1	no	—
53	C₂×D₁₇	—	111	1	no	Hall
54	C₂×C₅×D₃	—	629	1	no	Hall
55	C₃×C₁₇	C₂×C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
56	C₃₇	C₅×D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₁₇	—	111	1	no	—
58	D₁₇	—	111	1	no	—
59	D₁₇	C₅×D₁₁₁	1	1	yes	characteristic, direct product factor
60	C₂×C₃×C₅	—	17	1	no	—
61	C₅×D₃	—	37	1	no	—
62	C₅×D₃	—	629	1	no	—
63	C₂²×C₅	—	1887	1	no	Hall
64	C₁₇	C₂×C₅×D₁₁₁	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	D₁₇×D₃₇	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	629	1	no	Hall
67	C₂×C₅	—	17	1	no	—
68	C₂×C₅	—	1887	1	no	—
69	C₂×C₅	—	111	1	no	—
70	C₂×C₃	—	17	1	no	—
71	D₃	—	37	1	no	—
72	D₃	—	629	1	no	—
73	C₅	D₁₇×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²	—	1887	1	no	Sylow
75	C₃	C₅×D₁₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	17	1	no	—
77	C₂	—	1887	1	no	—
78	C₂	—	111	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₁₇×D₁₁₁
commutator, cosocle, hypocenter	C₃×C₁₇×C₃₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₇	C₂²
LCS	G ▷ C₃×C₁₇×C₃₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₁₈₈₇	C₂	semidirect
2. C₅×C₁₇×D₁₁₁	C₂	semidirect
3. C₃×C₅×D₁₇×C₃₇	C₂	semidirect
5. C₃×C₅×C₁₇×C₃₇	C₂²	semidirect
6. D₁₇×D₁₁₁	C₅	direct (N × H)
8. C₅×D₁₇×C₃₇	D₃	semidirect
10. D₁₈₈₇	C₂×C₅	semidirect
11. C₁₇×D₁₁₁	C₂×C₅	semidirect
12. C₃×D₁₇×C₃₇	C₂×C₅	semidirect
13. C₅×C₁₇×C₃₇	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₇	C₂²×C₅	semidirect
19. D₁₇×C₃₇	C₅×D₃	semidirect
22. C₅×D₁₁₁	D₁₇	direct (N × H)
25. C₁₇×C₃₇	C₂×C₅×D₃	semidirect
26. C₃×C₅×C₃₇	C₂×D₁₇	semidirect
29. C₃×C₅×D₁₇	D₃₇	semidirect
35. C₃×C₅×C₁₇	C₂×D₃₇	semidirect
38. D₁₁₁	C₅×D₁₇	direct (N × H)
40. C₅×C₃₇	D₃×D₁₇	semidirect
43. C₅×D₁₇	D₁₁₁	direct (N × H)
45. C₃×C₃₇	C₂×C₅×D₁₇	semidirect
47. C₃×D₁₇	C₅×D₃₇	semidirect
49. C₅×C₁₇	C₂×D₁₁₁	semidirect
55. C₃×C₁₇	C₂×C₅×D₃₇	semidirect
56. C₃₇	C₅×D₃×D₁₇	semidirect
59. D₁₇	C₅×D₁₁₁	direct (N × H)
64. C₁₇	C₂×C₅×D₁₁₁	semidirect
65. C₃×C₅	D₁₇×D₃₇	semidirect
73. C₅	D₁₇×D₁₁₁	direct (N × H)
75. C₃	C₅×D₁₇×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₁₈₈₇	2
C₅×C₁₇×D₁₁₁	2
C₃×C₅×D₁₇×C₃₇	2
C₅×D₁₇×D₃₇	3
D₁₇×D₁₁₁	5
C₂×C₅×D₁₁₁	17
C₅×D₃×D₁₇	37

Subgroups — C5×D17×D111 #49179857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₇×D₁₁₁ #49179857