Subgroups — C₃³×C₅×C₉×C₂₅ #72207166

Order 30375.

5544 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₅×C₂₅	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₉×C₂₅	C₃	1	39	yes	maximal, direct product factor
3	C₃³×C₅²×C₉	C₅	1	1	yes	maximal, characteristic
4	C₃³×C₉×C₂₅	C₅	1	5	yes	maximal, direct product factor
5	C₃³×C₅×C₂₅	C₉	1	27	yes	direct product factor
6	C₃³×C₅×C₂₅	C₃²	1	13	yes	—
7	C₃×C₅×C₉×C₂₅	C₃²	1	117	yes	direct product factor
8	C₃⁴×C₅²	C₃×C₅	1	1	yes	characteristic
9	C₃²×C₅²×C₉	C₃×C₅	1	39	yes	—
10	C₃⁴×C₂₅	C₃×C₅	1	5	yes	—
11	C₃²×C₉×C₂₅	C₃×C₅	1	195	yes	direct product factor
12	C₃³×C₅×C₉	C₂₅	1	5	yes	direct product factor
13	C₃³×C₅×C₉	C₅²	1	1	yes	characteristic
14	C₃²×C₅×C₂₅	C₃×C₉	1	117	yes	direct product factor
15	C₃²×C₅×C₂₅	C₃³	1	13	yes	—
16	C₅×C₉×C₂₅	C₃³	1	27	yes	direct product factor
17	C₃³×C₅²	C₅×C₉	1	27	yes	—
18	C₃³×C₅²	C₃²×C₅	1	13	yes	—
19	C₃×C₅²×C₉	C₃²×C₅	1	117	yes	—
20	C₃³×C₂₅	C₅×C₉	1	135	yes	direct product factor
21	C₃³×C₂₅	C₃²×C₅	1	65	yes	—
22	C₃×C₉×C₂₅	C₃²×C₅	1	585	yes	direct product factor
23	C₃⁴×C₅	C₃×C₂₅	1	5	yes	—
24	C₃⁴×C₅	C₃×C₅²	1	1	yes	characteristic
25	C₃²×C₅×C₉	C₃×C₂₅	1	195	yes	direct product factor
26	C₃²×C₅×C₉	C₃×C₅²	1	39	yes	—
27	C₃×C₅×C₂₅	C₃²×C₉	1	39	yes	direct product factor
28	C₃×C₅×C₂₅	C₃⁴	1	1	yes	characteristic
29	C₃³×C₉	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₃²×C₅²	C₃×C₅×C₉	1	117	yes	—
31	C₃²×C₅²	C₃³×C₅	1	13	yes	—
32	C₅²×C₉	C₃³×C₅	1	27	yes	—
33	C₃²×C₂₅	C₃×C₅×C₉	1	585	yes	direct product factor
34	C₃²×C₂₅	C₃³×C₅	1	65	yes	—
35	C₉×C₂₅	C₃³×C₅	1	135	yes	direct product factor
36	C₃³×C₅	C₉×C₂₅	1	135	yes	direct product factor
37	C₃³×C₅	C₃²×C₂₅	1	65	yes	—
38	C₃³×C₅	C₅²×C₉	1	27	yes	—
39	C₃³×C₅	C₃²×C₅²	1	13	yes	—
40	C₃×C₅×C₉	C₃²×C₂₅	1	585	yes	direct product factor
41	C₃×C₅×C₉	C₃²×C₅²	1	117	yes	—
42	C₅×C₂₅	C₃³×C₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₃⁴	C₃×C₅×C₂₅	1	1	yes	characteristic
44	C₃²×C₉	C₃×C₅×C₂₅	1	39	yes	direct product factor
45	C₃×C₅²	C₃²×C₅×C₉	1	39	yes	—
46	C₃×C₅²	C₃⁴×C₅	1	1	yes	characteristic
47	C₃×C₂₅	C₃²×C₅×C₉	1	195	yes	direct product factor
48	C₃×C₂₅	C₃⁴×C₅	1	5	yes	—
49	C₃²×C₅	C₃×C₉×C₂₅	1	585	yes	direct product factor
50	C₃²×C₅	C₃³×C₂₅	1	65	yes	—
51	C₃²×C₅	C₃×C₅²×C₉	1	117	yes	—
52	C₃²×C₅	C₃³×C₅²	1	13	yes	—
53	C₅×C₉	C₃³×C₂₅	1	135	yes	direct product factor
54	C₅×C₉	C₃³×C₅²	1	27	yes	—
55	C₃³	C₅×C₉×C₂₅	1	27	yes	direct product factor
56	C₃³	C₃²×C₅×C₂₅	1	13	yes	—
57	C₃×C₉	C₃²×C₅×C₂₅	1	117	yes	direct product factor
58	C₅²	C₃³×C₅×C₉	1	1	yes	characteristic
59	C₂₅	C₃³×C₅×C₉	1	5	yes	direct product factor
60	C₃×C₅	C₃²×C₉×C₂₅	1	195	yes	direct product factor
61	C₃×C₅	C₃⁴×C₂₅	1	5	yes	—
62	C₃×C₅	C₃²×C₅²×C₉	1	39	yes	—
63	C₃×C₅	C₃⁴×C₅²	1	1	yes	characteristic
64	C₃²	C₃×C₅×C₉×C₂₅	1	117	yes	direct product factor
65	C₃²	C₃³×C₅×C₂₅	1	13	yes	—
66	C₉	C₃³×C₅×C₂₅	1	27	yes	direct product factor
67	C₅	C₃³×C₉×C₂₅	1	5	yes	direct product factor
68	C₅	C₃³×C₅²×C₉	1	1	yes	characteristic
69	C₃	C₃²×C₅×C₉×C₂₅	1	39	yes	direct product factor
70	C₃	C₃⁴×C₅×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₃⁴×C₅²
socle, prime radical	C₃⁴×C₅²	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅×C₉×C₂₅	C₃	direct (N × H)
4. C₃³×C₉×C₂₅	C₅	direct (N × H)
5. C₃³×C₅×C₂₅	C₉	direct (N × H)
7. C₃×C₅×C₉×C₂₅	C₃²	direct (N × H)
11. C₃²×C₉×C₂₅	C₃×C₅	direct (N × H)
12. C₃³×C₅×C₉	C₂₅	direct (N × H)
14. C₃²×C₅×C₂₅	C₃×C₉	direct (N × H)
16. C₅×C₉×C₂₅	C₃³	direct (N × H)
20. C₃³×C₂₅	C₅×C₉	direct (N × H)
22. C₃×C₉×C₂₅	C₃²×C₅	direct (N × H)
25. C₃²×C₅×C₉	C₃×C₂₅	direct (N × H)
27. C₃×C₅×C₂₅	C₃²×C₉	direct (N × H)
29. C₃³×C₉	C₅×C₂₅	direct (N × H)
33. C₃²×C₂₅	C₃×C₅×C₉	direct (N × H)
35. C₉×C₂₅	C₃³×C₅	direct (N × H)
36. C₃³×C₅	C₉×C₂₅	direct (N × H)
40. C₃×C₅×C₉	C₃²×C₂₅	direct (N × H)
42. C₅×C₂₅	C₃³×C₉	direct (N × H)
44. C₃²×C₉	C₃×C₅×C₂₅	direct (N × H)
47. C₃×C₂₅	C₃²×C₅×C₉	direct (N × H)
49. C₃²×C₅	C₃×C₉×C₂₅	direct (N × H)
53. C₅×C₉	C₃³×C₂₅	direct (N × H)
55. C₃³	C₅×C₉×C₂₅	direct (N × H)
57. C₃×C₉	C₃²×C₅×C₂₅	direct (N × H)
59. C₂₅	C₃³×C₅×C₉	direct (N × H)
60. C₃×C₅	C₃²×C₉×C₂₅	direct (N × H)
64. C₃²	C₃×C₅×C₉×C₂₅	direct (N × H)
66. C₉	C₃³×C₅×C₂₅	direct (N × H)
67. C₅	C₃³×C₉×C₂₅	direct (N × H)
69. C₃	C₃²×C₅×C₉×C₂₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₅×C₂₅	3
C₃²×C₅×C₉×C₂₅	3
C₃³×C₅²×C₉	5
C₃³×C₉×C₂₅	5

Subgroups — C33×C5×C9×C25 #72207166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₅×C₉×C₂₅ #72207166