Subgroups — C₂×C₅²×C₇²×C₉ #36347784

Order 22050.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇²×C₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₅²×C₇²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₅×C₇²×C₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic
5	C₂×C₅²×C₇×C₉	C₇	1	8	yes	maximal, direct product factor
6	C₂×C₅²×C₇²	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₇²×C₉	C₂×C₅	1	6	yes	direct product factor
8	C₅²×C₇×C₉	C₂×C₇	1	8	yes	direct product factor
9	C₂×C₃×C₅×C₇²	C₃×C₅	1	6	yes	—
10	C₅²×C₇²	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₅²×C₇	C₃×C₇	1	8	yes	—
12	C₂×C₇²×C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇²	C₂×C₃×C₅	1	6	yes	—
14	C₂×C₅×C₇×C₉	C₅×C₇	1	48	yes	direct product factor
15	C₃×C₅²×C₇	C₂×C₃×C₇	1	8	yes	—
16	C₂×C₅×C₇²	C₅×C₉	1	6	yes	direct product factor
17	C₂×C₅²×C₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₇²×C₉	C₂×C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₅²×C₇	C₇×C₉	1	8	yes	direct product factor
20	C₅×C₇×C₉	C₂×C₅×C₇	1	48	yes	direct product factor
21	C₂×C₃×C₇²	C₃×C₅²	1	1	yes	characteristic
22	C₅×C₇²	C₂×C₅×C₉	1	6	yes	direct product factor
23	C₅²×C₉	C₂×C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₃×C₅×C₇	C₃×C₅×C₇	1	48	yes	—
25	C₅²×C₇	C₂×C₇×C₉	1	8	yes	direct product factor
26	C₂×C₃×C₅²	C₃×C₇²	1	1	yes	characteristic
27	C₃×C₇²	C₂×C₃×C₅²	1	1	yes	characteristic
28	C₂×C₇×C₉	C₅²×C₇	1	8	yes	direct product factor
29	C₃×C₅×C₇	C₂×C₃×C₅×C₇	1	48	yes	—
30	C₂×C₇²	C₅²×C₉	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₅×C₉	C₅×C₇²	1	6	yes	direct product factor
32	C₃×C₅²	C₂×C₃×C₇²	1	1	yes	characteristic
33	C₂×C₅×C₇	C₅×C₇×C₉	1	48	yes	direct product factor
34	C₇×C₉	C₂×C₅²×C₇	1	8	yes	direct product factor
35	C₂×C₅²	C₇²×C₉	1	1	yes	characteristic, direct product factor, Hall
36	C₇²	C₂×C₅²×C₉	1	1	yes	characteristic, direct product factor, Sylow
37	C₅×C₉	C₂×C₅×C₇²	1	6	yes	direct product factor
38	C₂×C₃×C₇	C₃×C₅²×C₇	1	8	yes	—
39	C₅×C₇	C₂×C₅×C₇×C₉	1	48	yes	direct product factor
40	C₂×C₃×C₅	C₃×C₅×C₇²	1	6	yes	—
41	C₅²	C₂×C₇²×C₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	C₂×C₃×C₅²×C₇	1	8	yes	—
43	C₂×C₉	C₅²×C₇²	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₅	C₂×C₃×C₅×C₇²	1	6	yes	—
45	C₂×C₇	C₅²×C₇×C₉	1	8	yes	direct product factor
46	C₂×C₅	C₅×C₇²×C₉	1	6	yes	direct product factor
47	C₉	C₂×C₅²×C₇²	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₂×C₅²×C₇×C₉	1	8	yes	direct product factor
49	C₂×C₃	C₃×C₅²×C₇²	1	1	yes	characteristic
50	C₅	C₂×C₅×C₇²×C₉	1	6	yes	direct product factor
51	C₃	C₂×C₃×C₅²×C₇²	1	1	yes	characteristic
52	C₂	C₅²×C₇²×C₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₅²×C₇²
socle, prime radical	C₂×C₃×C₅²×C₇²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇²×C₉	C₂	direct (N × H)
3. C₂×C₅×C₇²×C₉	C₅	direct (N × H)
5. C₂×C₅²×C₇×C₉	C₇	direct (N × H)
6. C₂×C₅²×C₇²	C₉	direct (N × H)
7. C₅×C₇²×C₉	C₂×C₅	direct (N × H)
8. C₅²×C₇×C₉	C₂×C₇	direct (N × H)
10. C₅²×C₇²	C₂×C₉	direct (N × H)
12. C₂×C₇²×C₉	C₅²	direct (N × H)
14. C₂×C₅×C₇×C₉	C₅×C₇	direct (N × H)
16. C₂×C₅×C₇²	C₅×C₉	direct (N × H)
17. C₂×C₅²×C₉	C₇²	direct (N × H)
18. C₇²×C₉	C₂×C₅²	direct (N × H)
19. C₂×C₅²×C₇	C₇×C₉	direct (N × H)
20. C₅×C₇×C₉	C₂×C₅×C₇	direct (N × H)
22. C₅×C₇²	C₂×C₅×C₉	direct (N × H)
23. C₅²×C₉	C₂×C₇²	direct (N × H)
25. C₅²×C₇	C₂×C₇×C₉	direct (N × H)
28. C₂×C₇×C₉	C₅²×C₇	direct (N × H)
30. C₂×C₇²	C₅²×C₉	direct (N × H)
31. C₂×C₅×C₉	C₅×C₇²	direct (N × H)
33. C₂×C₅×C₇	C₅×C₇×C₉	direct (N × H)
34. C₇×C₉	C₂×C₅²×C₇	direct (N × H)
35. C₂×C₅²	C₇²×C₉	direct (N × H)
36. C₇²	C₂×C₅²×C₉	direct (N × H)
37. C₅×C₉	C₂×C₅×C₇²	direct (N × H)
39. C₅×C₇	C₂×C₅×C₇×C₉	direct (N × H)
41. C₅²	C₂×C₇²×C₉	direct (N × H)
43. C₂×C₉	C₅²×C₇²	direct (N × H)
45. C₂×C₇	C₅²×C₇×C₉	direct (N × H)
46. C₂×C₅	C₅×C₇²×C₉	direct (N × H)
47. C₉	C₂×C₅²×C₇²	direct (N × H)
48. C₇	C₂×C₅²×C₇×C₉	direct (N × H)
50. C₅	C₂×C₅×C₇²×C₉	direct (N × H)
52. C₂	C₅²×C₇²×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
C₅²×C₇²×C₉	2
C₂×C₃×C₅²×C₇²	3
C₂×C₅×C₇²×C₉	5
C₂×C₅²×C₇×C₉	7

Subgroups — C2×C52×C72×C9 #36347784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅²×C₇²×C₉ #36347784