Subgroups — C₂×D₅×C₇⋊C₉ #11929465

Order 1260.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₇⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇×D₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₇⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₇⋊C₉	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₇	C₂×C₃	1	1	yes	characteristic
7	C₃×C₇×D₅	C₂×C₃	1	2	yes	—
8	C₂×C₉×D₅	—	7	1	no	maximal, Hall
9	C₂×C₇×D₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇⋊C₉	—	5	2	no	—
11	C₂×C₇⋊C₉	D₅	1	1	yes	characteristic, direct product factor
12	C₃×C₅×C₇	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₅×C₉	—	7	1	no	—
14	C₉×D₅	—	7	2	no	—
15	C₂²×C₃×C₇	—	5	1	no	—
16	C₂×C₅×C₇	C₂×C₉	1	1	yes	characteristic, complemented
17	C₇×D₅	C₂×C₉	1	2	yes	complemented
18	C₇⋊C₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×D₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₅×C₉	—	7	1	no	Hall
21	C₂×C₃×C₇	—	5	2	no	—
22	C₂×C₃×C₇	C₃×D₅	1	1	yes	characteristic
23	C₂²×C₉	—	35	1	no	Hall
24	C₅×C₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₅	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₃×D₅	C₂×ΓL(1,𝔽₈)	1	2	yes	—
27	C₂²×C₇	—	5	1	no	Hall
28	C₃×C₇	C₂×C₃×D₅	1	1	yes	characteristic
29	C₂×D₅	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₉	—	7	1	no	—
31	C₂×C₉	—	35	2	no	—
32	C₃×C₅	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₂×C₇	—	5	2	no	—
34	C₂×C₇	C₉×D₅	1	1	yes	characteristic, complemented
35	C₂²×C₃	—	5	1	no	—
36	C₂×C₅	C₂×C₇⋊C₉	1	1	yes	characteristic, complemented
37	D₅	C₂×C₇⋊C₉	1	2	yes	direct product factor
38	C₉	—	7	1	no	Sylow
39	C₇	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	—	5	2	no	—
41	C₂×C₃	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
42	C₅	C₂²×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	5	1	no	Sylow
44	C₃	C₂×D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic
45	C₂	—	5	2	no	—
46	C₂	D₅×C₇⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅×ΓL(1,𝔽₈)
commutator, hypocenter	C₅×C₇	C₂²×C₉
Frattini	C₃	C₂×D₅×ΓL(1,𝔽₈)
Fitting, socle	C₂×C₃×C₅×C₇	C₂×C₃
prime radical	C₂×C₃×C₇×D₅	C₃
cosocle	C₃×C₅×C₇	C₂²×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₇⋊C₉	C₂	semidirect
2. D₅×C₇⋊C₉	C₂	direct (N × H)
4. C₅×C₇⋊C₉	C₂²	semidirect
9. C₂×C₇×D₅	C₉	semidirect
11. C₂×C₇⋊C₉	D₅	direct (N × H)
16. C₂×C₅×C₇	C₂×C₉	semidirect
17. C₇×D₅	C₂×C₉	semidirect
18. C₇⋊C₉	C₂×D₅	direct (N × H)
24. C₅×C₇	C₂²×C₉	semidirect
29. C₂×D₅	C₇⋊C₉	direct (N × H)
34. C₂×C₇	C₉×D₅	semidirect
36. C₂×C₅	C₂×C₇⋊C₉	semidirect
37. D₅	C₂×C₇⋊C₉	direct (N × H)
39. C₇	C₂×C₉×D₅	semidirect
42. C₅	C₂²×C₇⋊C₉	semidirect
46. C₂	D₅×C₇⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇⋊C₉	2
D₅×C₇⋊C₉	2
C₂×C₃×C₇×D₅	3
C₂²×C₇⋊C₉	5
C₂×C₉×D₅	7

Subgroups — C2×D5×C7⋊C9 #11929465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₇⋊C₉ #11929465