Subgroups — C₉×D₅×D₁₇₃ #44528126

Order 31140.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₈₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₉×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×D₁₇₃	C₃	1	1	yes	maximal, characteristic
5	C₅×C₉×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₉×D₁₇₃	—	5	1	no	maximal, Hall
7	C₃×D₈₆₅	C₂×C₃	1	1	yes	characteristic
8	C₃×D₅×C₁₇₃	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅×D₁₇₃	C₂×C₃	1	1	yes	characteristic
10	D₅×D₁₇₃	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₉×D₁₇₃	—	5	1	no	—
12	C₉×D₁₇₃	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₉×C₁₇₃	—	5	1	no	—
14	C₃×C₅×C₁₇₃	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×D₁₇₃	—	5	1	no	—
16	D₈₆₅	C₂×C₉	1	1	yes	characteristic, complemented
17	C₅×D₁₇₃	C₂×C₉	1	1	yes	characteristic, complemented
18	D₅×C₁₇₃	C₂×C₉	1	1	yes	characteristic, complemented
19	C₉×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₇₃	—	5	1	no	—
21	C₃×D₁₇₃	—	5	1	no	—
22	C₃×D₁₇₃	C₃×D₅	1	1	yes	characteristic
23	C₅×C₁₇₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₇₃	—	5	1	no	Hall
25	C₃×C₁₇₃	C₂×C₃×D₅	1	1	yes	characteristic
26	C₂×C₁₇₃	—	5	1	no	—
27	D₁₇₃	—	5	1	no	—
28	D₁₇₃	C₉×D₅	1	1	yes	characteristic, direct product factor
29	C₂×C₉×D₅	—	173	1	no	maximal, Hall
30	C₁₇₃	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅×C₉	—	173	1	no	—
32	C₉×D₅	—	173	1	no	—
33	C₉×D₅	D₁₇₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃×D₅	—	173	1	no	—
35	C₅×C₉	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₉	—	865	1	no	Hall
37	C₂×C₃×C₅	—	173	1	no	—
38	C₃×D₅	—	173	1	no	—
39	C₃×D₅	C₃×D₁₇₃	1	1	yes	characteristic
40	C₂×D₅	—	173	1	no	Hall
41	C₂×C₉	—	5	1	no	—
42	C₂×C₉	—	865	1	no	—
43	C₂×C₉	—	173	1	no	—
44	C₃×C₅	C₂×C₃×D₁₇₃	1	1	yes	characteristic
45	C₂²×C₃	—	865	1	no	—
46	C₂×C₅	—	173	1	no	—
47	D₅	—	173	1	no	—
48	D₅	C₉×D₁₇₃	1	1	yes	characteristic, direct product factor
49	C₉	D₅×D₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃	—	5	1	no	—
51	C₂×C₃	—	865	1	no	—
52	C₂×C₃	—	173	1	no	—
53	C₅	C₂×C₉×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	865	1	no	Sylow
55	C₃	C₃×D₅×D₁₇₃	1	1	yes	characteristic
56	C₂	—	5	1	no	—
57	C₂	—	865	1	no	—
58	C₂	—	173	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₅×D₁₇₃
commutator, hypocenter	C₅×C₁₇₃	C₂²×C₉
Frattini	C₃	C₃×D₅×D₁₇₃
Fitting	C₅×C₉×C₁₇₃	C₂²
socle, cosocle	C₃×C₅×C₁₇₃	C₂²×C₃
prime radical	C₃×D₅×D₁₇₃	C₃
LCS	G ▷ C₅×C₁₇₃
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₈₆₅	C₂	semidirect
2. C₉×D₅×C₁₇₃	C₂	semidirect
3. C₅×C₉×D₁₇₃	C₂	semidirect
5. C₅×C₉×C₁₇₃	C₂²	semidirect
10. D₅×D₁₇₃	C₉	direct (N × H)
12. C₉×D₁₇₃	D₅	direct (N × H)
16. D₈₆₅	C₂×C₉	semidirect
17. C₅×D₁₇₃	C₂×C₉	semidirect
18. D₅×C₁₇₃	C₂×C₉	semidirect
19. C₉×C₁₇₃	C₂×D₅	semidirect
23. C₅×C₁₇₃	C₂²×C₉	semidirect
28. D₁₇₃	C₉×D₅	direct (N × H)
30. C₁₇₃	C₂×C₉×D₅	semidirect
33. C₉×D₅	D₁₇₃	direct (N × H)
35. C₅×C₉	C₂×D₁₇₃	semidirect
48. D₅	C₉×D₁₇₃	direct (N × H)
49. C₉	D₅×D₁₇₃	direct (N × H)
53. C₅	C₂×C₉×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₉×D₈₆₅	2
C₉×D₅×C₁₇₃	2
C₅×C₉×D₁₇₃	2
C₃×D₅×D₁₇₃	3
C₂×C₉×D₁₇₃	5
C₂×C₉×D₅	173

Subgroups — C9×D5×D173 #44528126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₅×D₁₇₃ #44528126