Subgroups — C₅×D₄×C₉ #67101

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉	—	2	2	no	—
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	D₄×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	2	yes	—
8	C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic
9	C₅×C₉	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₅×D₄	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉	C₂×C₅	1	2	yes	complemented
12	C₄×C₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	—	2	2	no	—
14	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
15	C₃×D₄	C₃×C₅	1	1	yes	characteristic
16	C₂²×C₅	C₂×C₉	1	2	yes	complemented
17	C₄×C₅	C₂×C₉	1	1	yes	characteristic, complemented
18	C₂×C₉	—	2	2	no	—
19	C₂×C₉	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅	C₃×D₄	1	1	yes	characteristic
21	C₂²×C₃	C₂×C₃×C₅	1	2	yes	—
22	C₃×C₄	C₂×C₃×C₅	1	1	yes	characteristic
23	C₂×C₅	—	2	2	no	—
24	C₂×C₅	C₂²×C₉	1	1	yes	characteristic
25	C₉	C₅×D₄	1	1	yes	characteristic, direct product factor, Sylow
26	D₄	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	2	2	no	—
28	C₂×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
29	C₅	D₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₂×C₅×C₉	1	2	yes	complemented
31	C₄	C₂×C₅×C₉	1	1	yes	characteristic, complemented
32	C₃	C₃×C₅×D₄	1	1	yes	characteristic
33	C₂	—	2	2	no	—
34	C₂	C₂²×C₅×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₉	C₂²
commutator	C₂	C₂²×C₅×C₉
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₅
socle	C₂×C₃×C₅	C₂²×C₃
prime radical	C₃×C₅×D₄	C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₉	C₂	semidirect
2. C₄×C₅×C₉	C₂	semidirect
6. D₄×C₉	C₅	direct (N × H)
9. C₅×C₉	D₄	direct (N × H)
10. C₅×D₄	C₉	direct (N × H)
11. C₂²×C₉	C₂×C₅	semidirect
12. C₄×C₉	C₂×C₅	semidirect
16. C₂²×C₅	C₂×C₉	semidirect
17. C₄×C₅	C₂×C₉	semidirect
25. C₉	C₅×D₄	direct (N × H)
26. D₄	C₅×C₉	direct (N × H)
29. C₅	D₄×C₉	direct (N × H)
30. C₂²	C₂×C₅×C₉	semidirect
31. C₄	C₂×C₅×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₉	2
C₄×C₅×C₉	2
C₃×C₅×D₄	3
D₄×C₉	5

Subgroups — C5×D4×C9 #67101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₄×C₉ #67101