Subgroups — C₅×D₉×C₂₉⋊C₇ #32912484

Order 18270.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₂₉⋊C₇	—	3	1	no	maximal
3	D₉×C₂₉⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₂₉⋊C₇	D₃	1	1	yes	characteristic
5	C₅×D₉×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₅×C₂₉⋊C₇	—	9	1	no	Hall
7	C₉×C₂₉⋊C₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
9	D₃×C₂₉⋊C₇	—	3	1	no	—
10	C₅×C₂₉⋊C₇	D₉	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₃×C₂₉	—	3	1	no	—
12	C₅×C₇×D₉	—	29	1	no	maximal, Hall
13	C₃×C₂₉⋊C₇	C₅×D₃	1	1	yes	characteristic
14	D₉×C₂₉	C₅×C₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₂₉	D₃×C₇	1	1	yes	characteristic
16	C₂×C₂₉⋊C₇	—	9	1	no	Hall
17	C₅×C₇×C₉	—	29	1	no	Hall
18	C₂×C₅×C₂₉	—	9	1	no	Hall
19	C₉×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
20	C₅×D₃×C₇	—	87	1	no	—
21	C₂₉⋊C₇	C₅×D₉	1	1	yes	characteristic, direct product factor, Hall
22	D₃×C₂₉	—	3	1	no	—
23	C₅×C₂₉	C₇×D₉	1	1	yes	characteristic, complemented, Hall
24	C₇×D₉	—	29	1	no	Hall
25	C₃×C₅×C₇	—	29	1	no	—
26	C₅×D₉	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
27	C₃×C₂₉	C₅×D₃×C₇	1	1	yes	characteristic
28	C₂×C₅×C₇	—	261	1	no	Hall
29	C₇×C₉	—	29	1	no	Hall
30	C₂×C₂₉	—	9	1	no	Hall
31	C₅×C₉	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
32	D₃×C₇	—	87	1	no	—
33	C₅×C₇	—	29	1	no	Hall
34	C₅×D₃	—	3	1	no	—
35	C₂₉	C₅×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	—	29	1	no	—
37	D₉	C₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅	D₃×C₂₉⋊C₇	1	1	yes	characteristic
39	C₂×C₇	—	261	1	no	Hall
40	C₂×C₅	—	9	1	no	Hall
41	C₉	C₂×C₅×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	29	1	no	Sylow
43	D₃	—	3	1	no	—
44	C₅	D₉×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×D₃×C₂₉⋊C₇	1	1	yes	characteristic
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₉×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₉×C₂₉	C₂×C₅×C₇
Frattini	C₃	C₅×D₃×C₂₉⋊C₇
Fitting	C₅×C₉×C₂₉	C₂×C₇
socle	C₃×C₅×C₂₉	D₃×C₇
LCS	G ▷ C₉×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₂₉⋊C₇	C₂	semidirect
3. D₉×C₂₉⋊C₇	C₅	direct (N × H)
5. C₅×D₉×C₂₉	C₇	semidirect
7. C₉×C₂₉⋊C₇	C₂×C₅	semidirect
8. C₅×C₉×C₂₉	C₂×C₇	semidirect
10. C₅×C₂₉⋊C₇	D₉	direct (N × H)
14. D₉×C₂₉	C₅×C₇	semidirect
19. C₉×C₂₉	C₂×C₅×C₇	semidirect
21. C₂₉⋊C₇	C₅×D₉	direct (N × H)
23. C₅×C₂₉	C₇×D₉	semidirect
26. C₅×D₉	C₂₉⋊C₇	direct (N × H)
31. C₅×C₉	C₂×C₂₉⋊C₇	semidirect
35. C₂₉	C₅×C₇×D₉	semidirect
37. D₉	C₅×C₂₉⋊C₇	direct (N × H)
41. C₉	C₂×C₅×C₂₉⋊C₇	semidirect
44. C₅	D₉×C₂₉⋊C₇	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×C₉×C₂₉⋊C₇	2
C₅×D₃×C₂₉⋊C₇	3
D₉×C₂₉⋊C₇	5
C₅×D₉×C₂₉	7
C₅×C₇×D₉	29

Subgroups — C5×D9×C29⋊C7 #32912484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₉×C₂₉⋊C₇ #32912484