Subgroups — C₂⁵×C₅×C₉ #13088272

Order 1440.

2244 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₉	C₂	1	31	yes	maximal, direct product factor
2	C₂⁵×C₃×C₅	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₅×C₉	C₂²	1	155	yes	direct product factor
4	C₂⁵×C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₃×C₅	C₂×C₃	1	31	yes	—
6	C₂²×C₅×C₉	C₂³	1	155	yes	direct product factor
7	C₂⁵×C₅	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂⁴×C₉	C₂×C₅	1	31	yes	direct product factor
9	C₂³×C₃×C₅	C₂²×C₃	1	155	yes	—
10	C₂⁵×C₃	C₃×C₅	1	1	yes	characteristic
11	C₂×C₅×C₉	C₂⁴	1	31	yes	direct product factor
12	C₂⁴×C₅	C₂×C₉	1	31	yes	direct product factor
13	C₂³×C₉	C₂²×C₅	1	155	yes	direct product factor
14	C₂²×C₃×C₅	C₂³×C₃	1	155	yes	—
15	C₂⁴×C₃	C₂×C₃×C₅	1	31	yes	—
16	C₅×C₉	C₂⁵	1	1	yes	characteristic, direct product factor, Hall
17	C₂³×C₅	C₂²×C₉	1	155	yes	direct product factor
18	C₂²×C₉	C₂³×C₅	1	155	yes	direct product factor
19	C₂⁵	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₅	C₂⁴×C₃	1	31	yes	—
21	C₂³×C₃	C₂²×C₃×C₅	1	155	yes	—
22	C₂²×C₅	C₂³×C₉	1	155	yes	direct product factor
23	C₂×C₉	C₂⁴×C₅	1	31	yes	direct product factor
24	C₂⁴	C₂×C₅×C₉	1	31	yes	direct product factor
25	C₃×C₅	C₂⁵×C₃	1	1	yes	characteristic
26	C₂²×C₃	C₂³×C₃×C₅	1	155	yes	—
27	C₂×C₅	C₂⁴×C₉	1	31	yes	direct product factor
28	C₉	C₂⁵×C₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂³	C₂²×C₅×C₉	1	155	yes	direct product factor
30	C₂×C₃	C₂⁴×C₃×C₅	1	31	yes	—
31	C₅	C₂⁵×C₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₂²	C₂³×C₅×C₉	1	155	yes	direct product factor
33	C₃	C₂⁵×C₃×C₅	1	1	yes	characteristic
34	C₂	C₂⁴×C₅×C₉	1	31	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂⁵×C₃×C₅
socle, prime radical	C₂⁵×C₃×C₅	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₉	C₂	direct (N × H)
3. C₂³×C₅×C₉	C₂²	direct (N × H)
4. C₂⁵×C₉	C₅	direct (N × H)
6. C₂²×C₅×C₉	C₂³	direct (N × H)
7. C₂⁵×C₅	C₉	direct (N × H)
8. C₂⁴×C₉	C₂×C₅	direct (N × H)
11. C₂×C₅×C₉	C₂⁴	direct (N × H)
12. C₂⁴×C₅	C₂×C₉	direct (N × H)
13. C₂³×C₉	C₂²×C₅	direct (N × H)
16. C₅×C₉	C₂⁵	direct (N × H)
17. C₂³×C₅	C₂²×C₉	direct (N × H)
18. C₂²×C₉	C₂³×C₅	direct (N × H)
19. C₂⁵	C₅×C₉	direct (N × H)
22. C₂²×C₅	C₂³×C₉	direct (N × H)
23. C₂×C₉	C₂⁴×C₅	direct (N × H)
24. C₂⁴	C₂×C₅×C₉	direct (N × H)
27. C₂×C₅	C₂⁴×C₉	direct (N × H)
28. C₉	C₂⁵×C₅	direct (N × H)
29. C₂³	C₂²×C₅×C₉	direct (N × H)
31. C₅	C₂⁵×C₉	direct (N × H)
32. C₂²	C₂³×C₅×C₉	direct (N × H)
34. C₂	C₂⁴×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
C₂⁴×C₅×C₉	2
C₂⁵×C₃×C₅	3
C₂⁵×C₉	5

Subgroups — C25×C5×C9 #13088272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁵×C₅×C₉ #13088272