Subgroups — C₃×C₁₇×D₃₆₅ #49151908

Order 37230.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₃₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×D₇₃	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₇₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₇₃	—	5	1	no	Hall
7	C₃×D₃₆₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₇₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	D₃₆₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₅×C₁₇	—	73	1	no	maximal, Hall
12	C₃×D₇₃	—	5	1	no	Hall
13	C₅×C₇₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₇	D₇₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇₃	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
16	D₅×C₁₇	—	73	1	no	Hall
17	D₇₃	—	5	1	no	Hall
18	C₂×C₃×C₁₇	—	365	1	no	Hall
19	C₅×C₁₇	C₃×D₇₃	1	1	yes	characteristic, complemented, Hall
20	C₇₃	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₇	D₃₆₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	—	365	1	no	Hall
23	C₃×D₅	—	73	1	no	Hall
24	C₁₇	C₃×D₃₆₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₁₇×D₇₃	1	1	yes	characteristic, complemented, Hall
26	D₅	—	73	1	no	Hall
27	C₂×C₃	—	365	1	no	Hall
28	C₅	C₃×C₁₇×D₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₇×D₃₆₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	365	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₃₆₅
commutator, cosocle, hypocenter	C₅×C₇₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₇₃	C₂
LCS	G ▷ C₅×C₇₃
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₇₃	C₂	semidirect
2. C₁₇×D₃₆₅	C₃	direct (N × H)
4. C₅×C₁₇×C₇₃	C₂×C₃	semidirect
5. C₃×C₁₇×C₇₃	D₅	semidirect
7. C₃×D₃₆₅	C₁₇	direct (N × H)
8. C₁₇×C₇₃	C₃×D₅	semidirect
9. C₃×C₅×C₇₃	C₂×C₁₇	semidirect
10. D₃₆₅	C₃×C₁₇	direct (N × H)
13. C₅×C₇₃	C₂×C₃×C₁₇	semidirect
14. C₃×C₅×C₁₇	D₇₃	semidirect
15. C₃×C₇₃	D₅×C₁₇	semidirect
19. C₅×C₁₇	C₃×D₇₃	semidirect
20. C₇₃	C₃×D₅×C₁₇	semidirect
21. C₃×C₁₇	D₃₆₅	direct (N × H)
24. C₁₇	C₃×D₃₆₅	direct (N × H)
25. C₃×C₅	C₁₇×D₇₃	semidirect
28. C₅	C₃×C₁₇×D₇₃	semidirect
29. C₃	C₁₇×D₃₆₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₇×C₇₃	2
C₁₇×D₃₆₅	3
C₃×C₁₇×D₇₃	5
C₃×D₃₆₅	17
C₃×D₅×C₁₇	73

Subgroups — C3×C17×D365 #49151908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₃₆₅ #49151908