Subgroups — C₅×C₃⋊D₆₀₉ #32912528

Order 18270.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₀₉	—	3	4	no	maximal
3	C₃⋊D₆₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₂₉	D₃	1	4	yes	complemented
5	C₅×C₃⋊D₈₇	—	7	1	no	maximal, Hall
6	C₅×D₂₀₃	—	9	1	no	Hall
7	C₃²×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₅×C₂₉	D₇	1	1	yes	characteristic, complemented, Hall
9	D₆₀₉	—	3	4	no	—
10	C₅×C₇×C₂₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₈₇	—	21	4	no	—
12	C₅×C₃⋊D₂₁	—	29	1	no	maximal, Hall
13	C₃×C₇×C₂₉	C₅×D₃	1	4	yes	complemented
14	C₃⋊D₈₇	—	7	1	no	Hall
15	C₃×C₅×C₂₉	D₂₁	1	4	yes	complemented
16	D₂₀₃	—	9	1	no	Hall
17	C₃²×C₅×C₇	D₂₉	1	1	yes	characteristic, complemented, Hall
18	C₅×D₂₉	—	63	1	no	Hall
19	C₃²×C₂₉	C₅×D₇	1	1	yes	characteristic, complemented, Hall
20	C₅×D₂₁	—	87	4	no	—
21	C₇×C₂₉	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	D₈₇	—	21	4	no	—
23	C₅×C₂₉	C₃⋊D₂₁	1	1	yes	characteristic, complemented, Hall
24	C₃⋊D₂₁	—	29	1	no	Hall
25	C₃×C₅×C₇	D₈₇	1	4	yes	complemented
26	C₅×C₃⋊D₃	—	203	1	no	Hall
27	C₃×C₂₉	C₅×D₂₁	1	4	yes	complemented
28	C₅×D₇	—	261	1	no	Hall
29	C₃²×C₇	C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
30	D₂₉	—	63	1	no	Hall
31	C₃²×C₅	D₂₀₃	1	1	yes	characteristic, complemented, Hall
32	D₂₁	—	87	4	no	—
33	C₅×C₇	C₃⋊D₈₇	1	1	yes	characteristic, complemented, Hall
34	C₅×D₃	—	609	4	no	—
35	C₂₉	C₅×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	C₅×D₈₇	1	4	yes	complemented
37	C₃⋊D₃	—	203	1	no	Hall
38	C₃×C₅	D₆₀₉	1	4	yes	complemented
39	D₇	—	261	1	no	Hall
40	C₂×C₅	—	1827	1	no	Hall
41	C₃²	C₅×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₅×C₃⋊D₈₇	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	609	4	no	—
44	C₅	C₃⋊D₆₀₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₆₀₉	1	4	yes	complemented
46	C₂	—	1827	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊D₆₀₉
commutator, cosocle, hypocenter	C₃²×C₇×C₂₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₃²×C₇×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×C₂₉	C₂	semidirect
3. C₃⋊D₆₀₉	C₅	direct (N × H)
4. C₃×C₅×C₇×C₂₉	D₃	semidirect
7. C₃²×C₇×C₂₉	C₂×C₅	semidirect
8. C₃²×C₅×C₂₉	D₇	semidirect
10. C₅×C₇×C₂₉	C₃⋊D₃	semidirect
13. C₃×C₇×C₂₉	C₅×D₃	semidirect
15. C₃×C₅×C₂₉	D₂₁	semidirect
17. C₃²×C₅×C₇	D₂₉	semidirect
19. C₃²×C₂₉	C₅×D₇	semidirect
21. C₇×C₂₉	C₅×C₃⋊D₃	semidirect
23. C₅×C₂₉	C₃⋊D₂₁	semidirect
25. C₃×C₅×C₇	D₈₇	semidirect
27. C₃×C₂₉	C₅×D₂₁	semidirect
29. C₃²×C₇	C₅×D₂₉	semidirect
31. C₃²×C₅	D₂₀₃	semidirect
33. C₅×C₇	C₃⋊D₈₇	semidirect
35. C₂₉	C₅×C₃⋊D₂₁	semidirect
36. C₃×C₇	C₅×D₈₇	semidirect
38. C₃×C₅	D₆₀₉	semidirect
41. C₃²	C₅×D₂₀₃	semidirect
42. C₇	C₅×C₃⋊D₈₇	semidirect
44. C₅	C₃⋊D₆₀₉	direct (N × H)
45. C₃	C₅×D₆₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₇×C₂₉	2
C₅×D₆₀₉	3
C₃⋊D₆₀₉	5
C₅×C₃⋊D₈₇	7
C₅×C₃⋊D₂₁	29

Subgroups — C5×C3⋊D609 #32912528

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊D₆₀₉ #32912528