Subgroups — C₃²×D₅×D₁₇₃ #44528176

Order 31140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₈₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×D₁₇₃	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃²×D₁₇₃	—	5	1	no	maximal, Hall
7	C₃×D₈₆₅	C₂×C₃	1	4	yes	complemented
8	C₃×D₅×C₁₇₃	C₂×C₃	1	4	yes	complemented
9	C₃×C₅×D₁₇₃	C₂×C₃	1	4	yes	complemented
10	D₅×D₁₇₃	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×D₁₇₃	—	5	1	no	—
12	C₃²×D₁₇₃	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₃²×C₁₇₃	—	5	1	no	—
14	C₃×C₅×C₁₇₃	C₂²×C₃	1	4	yes	complemented
15	C₂×C₃×D₁₇₃	—	5	4	no	—
16	D₈₆₅	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₅×D₁₇₃	C₂×C₃²	1	1	yes	characteristic, complemented
18	D₅×C₁₇₃	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₃²×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₇₃	—	5	4	no	—
21	C₃×D₁₇₃	—	5	4	no	—
22	C₃×D₁₇₃	C₃×D₅	1	4	yes	direct product factor
23	C₅×C₁₇₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₇₃	—	5	1	no	Hall
25	C₃×C₁₇₃	C₂×C₃×D₅	1	4	yes	complemented
26	C₂×C₁₇₃	—	5	1	no	—
27	D₁₇₃	—	5	1	no	—
28	D₁₇₃	C₃²×D₅	1	1	yes	characteristic, direct product factor
29	C₂×C₃²×D₅	—	173	1	no	maximal, Hall
30	C₁₇₃	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃²×C₅	—	173	1	no	—
32	C₃²×D₅	—	173	1	no	—
33	C₃²×D₅	D₁₇₃	1	1	yes	characteristic, direct product factor
34	C₂×C₃×D₅	—	173	4	no	—
35	C₃²×C₅	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₃²	—	865	1	no	Hall
37	C₂×C₃×C₅	—	173	4	no	—
38	C₃×D₅	—	173	4	no	—
39	C₃×D₅	C₃×D₁₇₃	1	4	yes	direct product factor
40	C₂×D₅	—	173	1	no	Hall
41	C₂×C₃²	—	5	1	no	—
42	C₂×C₃²	—	865	1	no	—
43	C₂×C₃²	—	173	1	no	—
44	C₃×C₅	C₂×C₃×D₁₇₃	1	4	yes	complemented
45	C₂²×C₃	—	865	4	no	—
46	C₂×C₅	—	173	1	no	—
47	D₅	—	173	1	no	—
48	D₅	C₃²×D₁₇₃	1	1	yes	characteristic, direct product factor
49	C₃²	D₅×D₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃	—	5	4	no	—
51	C₂×C₃	—	865	4	no	—
52	C₂×C₃	—	173	4	no	—
53	C₅	C₂×C₃²×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	865	1	no	Sylow
55	C₃	C₃×D₅×D₁₇₃	1	4	yes	direct product factor
56	C₂	—	5	1	no	—
57	C₂	—	865	1	no	—
58	C₂	—	173	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	D₅×D₁₇₃
commutator, cosocle, hypocenter	C₅×C₁₇₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₇₃	C₂²
LCS	G ▷ C₅×C₁₇₃
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×D₁₇₃	C₂	semidirect
2. C₃²×D₅×C₁₇₃	C₂	semidirect
3. C₃²×D₈₆₅	C₂	semidirect
4. C₃×D₅×D₁₇₃	C₃	direct (N × H)
5. C₃²×C₅×C₁₇₃	C₂²	semidirect
7. C₃×D₈₆₅	C₂×C₃	semidirect
8. C₃×D₅×C₁₇₃	C₂×C₃	semidirect
9. C₃×C₅×D₁₇₃	C₂×C₃	semidirect
10. D₅×D₁₇₃	C₃²	direct (N × H)
12. C₃²×D₁₇₃	D₅	direct (N × H)
14. C₃×C₅×C₁₇₃	C₂²×C₃	semidirect
16. D₈₆₅	C₂×C₃²	semidirect
17. C₅×D₁₇₃	C₂×C₃²	semidirect
18. D₅×C₁₇₃	C₂×C₃²	semidirect
19. C₃²×C₁₇₃	C₂×D₅	semidirect
22. C₃×D₁₇₃	C₃×D₅	direct (N × H)
23. C₅×C₁₇₃	C₂²×C₃²	semidirect
25. C₃×C₁₇₃	C₂×C₃×D₅	semidirect
28. D₁₇₃	C₃²×D₅	direct (N × H)
30. C₁₇₃	C₂×C₃²×D₅	semidirect
33. C₃²×D₅	D₁₇₃	direct (N × H)
35. C₃²×C₅	C₂×D₁₇₃	semidirect
39. C₃×D₅	C₃×D₁₇₃	direct (N × H)
44. C₃×C₅	C₂×C₃×D₁₇₃	semidirect
48. D₅	C₃²×D₁₇₃	direct (N × H)
49. C₃²	D₅×D₁₇₃	direct (N × H)
53. C₅	C₂×C₃²×D₁₇₃	semidirect
55. C₃	C₃×D₅×D₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₁₇₃	2
C₃²×D₅×C₁₇₃	2
C₃²×D₈₆₅	2
C₃×D₅×D₁₇₃	3
C₂×C₃²×D₁₇₃	5
C₂×C₃²×D₅	173

Subgroups — C32×D5×D173 #44528176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₅×D₁₇₃ #44528176