Subgroups — C₃×C₁₇×D₁₄₅ #28414404

Order 14790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₁₄₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₇×D₂₉	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₂₉	D₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₂₉	—	5	1	no	Hall
7	C₃×D₁₄₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×D₅×C₁₇	—	29	1	no	maximal, Hall
9	C₁₇×C₂₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₁₄₅	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₅×C₁₇	D₂₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₉	—	5	1	no	Hall
14	D₅×C₁₇	—	29	1	no	Hall
15	C₅×C₂₉	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₇	—	145	1	no	Hall
17	C₃×C₂₉	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₅×C₁₇	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
19	D₂₉	—	5	1	no	Hall
20	C₃×C₁₇	D₁₄₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₇	—	145	1	no	Hall
22	C₃×D₅	—	29	1	no	Hall
23	C₂₉	C₃×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
24	C₁₇	C₃×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₁₇×D₂₉	1	1	yes	characteristic, complemented, Hall
26	D₅	—	29	1	no	Hall
27	C₂×C₃	—	145	1	no	Hall
28	C₅	C₃×C₁₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₁₇×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	145	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₁₄₅
commutator, cosocle, hypocenter	C₅×C₂₉	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₂₉	C₂
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₂₉	C₂	semidirect
2. C₁₇×D₁₄₅	C₃	direct (N × H)
4. C₅×C₁₇×C₂₉	C₂×C₃	semidirect
5. C₃×C₁₇×C₂₉	D₅	semidirect
7. C₃×D₁₄₅	C₁₇	direct (N × H)
9. C₁₇×C₂₉	C₃×D₅	semidirect
10. C₃×C₅×C₂₉	C₂×C₁₇	semidirect
11. D₁₄₅	C₃×C₁₇	direct (N × H)
12. C₃×C₅×C₁₇	D₂₉	semidirect
15. C₅×C₂₉	C₂×C₃×C₁₇	semidirect
17. C₃×C₂₉	D₅×C₁₇	semidirect
18. C₅×C₁₇	C₃×D₂₉	semidirect
20. C₃×C₁₇	D₁₄₅	direct (N × H)
23. C₂₉	C₃×D₅×C₁₇	semidirect
24. C₁₇	C₃×D₁₄₅	direct (N × H)
25. C₃×C₅	C₁₇×D₂₉	semidirect
28. C₅	C₃×C₁₇×D₂₉	semidirect
29. C₃	C₁₇×D₁₄₅	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×C₂₉	2
C₁₇×D₁₄₅	3
C₃×C₁₇×D₂₉	5
C₃×D₁₄₅	17
C₃×D₅×C₁₇	29

Subgroups — C3×C17×D145 #28414404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₇×D₁₄₅ #28414404