Subgroups — C₂×C₄×C₅×C₉ #67100

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	1	yes	maximal, characteristic
2	C₄×C₅×C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₄×C₅	C₃	1	1	yes	maximal, characteristic
4	C₂×C₅×C₉	C₄	1	2	yes	direct product factor
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₄×C₅	C₂×C₃	1	2	yes	—
9	C₅×C₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₄×C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₉	C₂×C₅	1	1	yes	characteristic
12	C₄×C₉	C₂×C₅	1	2	yes	direct product factor
13	C₂×C₃×C₅	C₃×C₄	1	2	yes	—
14	C₂×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄	C₃×C₅	1	1	yes	characteristic
16	C₂²×C₅	C₂×C₉	1	1	yes	characteristic
17	C₄×C₅	C₂×C₉	1	2	yes	direct product factor
18	C₂×C₉	C₄×C₅	1	2	yes	direct product factor
19	C₂×C₉	C₂²×C₅	1	1	yes	characteristic
20	C₃×C₅	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃	C₂×C₃×C₅	1	1	yes	characteristic
22	C₃×C₄	C₂×C₃×C₅	1	2	yes	—
23	C₂×C₅	C₄×C₉	1	2	yes	direct product factor
24	C₂×C₅	C₂²×C₉	1	1	yes	characteristic
25	C₉	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₄	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	C₃×C₄×C₅	1	2	yes	—
28	C₂×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
29	C₅	C₂×C₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₂×C₅×C₉	1	1	yes	characteristic
31	C₄	C₂×C₅×C₉	1	2	yes	direct product factor
32	C₃	C₂×C₃×C₄×C₅	1	1	yes	characteristic
33	C₂	C₄×C₅×C₉	1	2	yes	direct product factor
34	C₂	C₂²×C₅×C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×C₉	C₂	direct (N × H)
4. C₂×C₅×C₉	C₄	direct (N × H)
6. C₂×C₄×C₉	C₅	direct (N × H)
9. C₅×C₉	C₂×C₄	direct (N × H)
10. C₂×C₄×C₅	C₉	direct (N × H)
12. C₄×C₉	C₂×C₅	direct (N × H)
17. C₄×C₅	C₂×C₉	direct (N × H)
18. C₂×C₉	C₄×C₅	direct (N × H)
23. C₂×C₅	C₄×C₉	direct (N × H)
25. C₉	C₂×C₄×C₅	direct (N × H)
26. C₂×C₄	C₅×C₉	direct (N × H)
29. C₅	C₂×C₄×C₉	direct (N × H)
31. C₄	C₂×C₅×C₉	direct (N × H)
33. C₂	C₄×C₅×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
C₂²×C₅×C₉	2
C₄×C₅×C₉	2
C₂×C₃×C₄×C₅	3
C₂×C₄×C₉	5

Subgroups — C2×C4×C5×C9 #67100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₉ #67100