Subgroups — C₂×C₅×C₃⋊D₃×C₁₇₃ #44528219

Order 31140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃×C₁₇₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₁₇₃	—	3	4	no	maximal
4	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₃×C₁₇₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₁₇₃	—	3	8	no	—
7	C₂×C₃×C₅×C₁₇₃	D₃	1	4	yes	complemented
8	C₂²×C₅×C₁₇₃	—	9	1	no	Hall
9	C₃⋊D₃×C₁₇₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃²×C₁₇₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₇₃	C₂×D₃	1	4	yes	complemented
12	C₂×D₃×C₁₇₃	—	3	4	no	—
13	C₂×C₅×C₁₇₃	—	9	2	no	—
14	C₂×C₅×C₁₇₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃²×C₁₇₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₇₃	C₅×D₃	1	4	yes	complemented
17	D₃×C₁₇₃	—	3	8	no	—
18	C₅×C₁₇₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₁₇₃	—	9	1	no	Hall
20	C₃×C₁₇₃	C₂×C₅×D₃	1	4	yes	complemented
21	C₂×C₁₇₃	—	9	2	no	—
22	C₂×C₁₇₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
23	C₂×C₅×C₃⋊D₃	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₇₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃²×C₅	C₂×C₁₇₃	1	1	yes	characteristic, complemented
26	C₅×C₃⋊D₃	C₂×C₁₇₃	1	2	yes	direct product factor
27	C₂×C₅×D₃	—	3	4	no	—
28	C₃²×C₅	C₂²×C₁₇₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃⋊D₃	C₅×C₁₇₃	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₅	D₃×C₁₇₃	1	4	yes	complemented
31	C₅×D₃	—	3	8	no	—
32	C₂²×C₅	—	9	1	no	Hall
33	C₂×C₃²	C₂×C₅×C₁₇₃	1	1	yes	characteristic, complemented
34	C₃⋊D₃	C₂×C₅×C₁₇₃	1	2	yes	direct product factor
35	C₃×C₅	C₂×D₃×C₁₇₃	1	4	yes	complemented
36	C₂×D₃	—	3	4	no	—
37	C₂×C₅	—	9	2	no	—
38	C₂×C₅	C₃⋊D₃×C₁₇₃	1	1	yes	characteristic, direct product factor
39	C₃²	C₂²×C₅×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₅×D₃×C₁₇₃	1	4	yes	complemented
41	D₃	—	3	8	no	—
42	C₅	C₂×C₃⋊D₃×C₁₇₃	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×C₅×D₃×C₁₇₃	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₅×C₃⋊D₃×C₁₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₇₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₇₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₁₇₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₃⋊D₃×C₁₇₃	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₇₃	C₂	semidirect
4. C₃²×C₅×C₁₇₃	C₂²	semidirect
5. C₂×C₃⋊D₃×C₁₇₃	C₅	direct (N × H)
7. C₂×C₃×C₅×C₁₇₃	D₃	semidirect
9. C₃⋊D₃×C₁₇₃	C₂×C₅	direct (N × H)
10. C₂×C₃²×C₁₇₃	C₂×C₅	semidirect
11. C₃×C₅×C₁₇₃	C₂×D₃	semidirect
14. C₂×C₅×C₁₇₃	C₃⋊D₃	direct (N × H)
15. C₃²×C₁₇₃	C₂²×C₅	semidirect
16. C₂×C₃×C₁₇₃	C₅×D₃	semidirect
18. C₅×C₁₇₃	C₂×C₃⋊D₃	direct (N × H)
20. C₃×C₁₇₃	C₂×C₅×D₃	semidirect
22. C₂×C₁₇₃	C₅×C₃⋊D₃	direct (N × H)
23. C₂×C₅×C₃⋊D₃	C₁₇₃	direct (N × H)
24. C₁₇₃	C₂×C₅×C₃⋊D₃	direct (N × H)
25. C₂×C₃²×C₅	C₂×C₁₇₃	semidirect
26. C₅×C₃⋊D₃	C₂×C₁₇₃	direct (N × H)
28. C₃²×C₅	C₂²×C₁₇₃	semidirect
29. C₂×C₃⋊D₃	C₅×C₁₇₃	direct (N × H)
30. C₂×C₃×C₅	D₃×C₁₇₃	semidirect
33. C₂×C₃²	C₂×C₅×C₁₇₃	semidirect
34. C₃⋊D₃	C₂×C₅×C₁₇₃	direct (N × H)
35. C₃×C₅	C₂×D₃×C₁₇₃	semidirect
38. C₂×C₅	C₃⋊D₃×C₁₇₃	direct (N × H)
39. C₃²	C₂²×C₅×C₁₇₃	semidirect
40. C₂×C₃	C₅×D₃×C₁₇₃	semidirect
42. C₅	C₂×C₃⋊D₃×C₁₇₃	direct (N × H)
44. C₃	C₂×C₅×D₃×C₁₇₃	semidirect
46. C₂	C₅×C₃⋊D₃×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₃⋊D₃×C₁₇₃	2
C₂×C₃²×C₅×C₁₇₃	2
C₂×C₅×D₃×C₁₇₃	3
C₂×C₃⋊D₃×C₁₇₃	5
C₂×C₅×C₃⋊D₃	173

Subgroups — C2×C5×C3⋊D3×C173 #44528219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₃⋊D₃×C₁₇₃ #44528219