Subgroups — C₂⁶×C₉×C₂₅ #72192579

Order 14400.

25425 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₉×C₂₅	C₂	1	63	yes	maximal, direct product factor
2	C₂⁶×C₃×C₂₅	C₃	1	1	yes	maximal, characteristic
3	C₂⁴×C₉×C₂₅	C₂²	1	651	yes	direct product factor
4	C₂⁶×C₅×C₉	C₅	1	1	yes	maximal, characteristic
5	C₂⁵×C₃×C₂₅	C₂×C₃	1	63	yes	—
6	C₂³×C₉×C₂₅	C₂³	1	1395	yes	direct product factor
7	C₂⁶×C₂₅	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂⁵×C₅×C₉	C₂×C₅	1	63	yes	—
9	C₂⁴×C₃×C₂₅	C₂²×C₃	1	651	yes	—
10	C₂⁶×C₃×C₅	C₃×C₅	1	1	yes	characteristic
11	C₂²×C₉×C₂₅	C₂⁴	1	651	yes	direct product factor
12	C₂⁵×C₂₅	C₂×C₉	1	63	yes	direct product factor
13	C₂⁴×C₅×C₉	C₂²×C₅	1	651	yes	—
14	C₂³×C₃×C₂₅	C₂³×C₃	1	1395	yes	—
15	C₂⁶×C₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂⁵×C₃×C₅	C₂×C₃×C₅	1	63	yes	—
17	C₂×C₉×C₂₅	C₂⁵	1	63	yes	direct product factor
18	C₂⁴×C₂₅	C₂²×C₉	1	651	yes	direct product factor
19	C₂³×C₅×C₉	C₂³×C₅	1	1395	yes	—
20	C₂⁶×C₅	C₅×C₉	1	1	yes	characteristic
21	C₂²×C₃×C₂₅	C₂⁴×C₃	1	651	yes	—
22	C₂⁵×C₉	C₂×C₂₅	1	63	yes	direct product factor
23	C₂⁴×C₃×C₅	C₂²×C₃×C₅	1	651	yes	—
24	C₉×C₂₅	C₂⁶	1	1	yes	characteristic, direct product factor, Hall
25	C₂³×C₂₅	C₂³×C₉	1	1395	yes	direct product factor
26	C₂⁶×C₃	C₃×C₂₅	1	1	yes	characteristic
27	C₂²×C₅×C₉	C₂⁴×C₅	1	651	yes	—
28	C₂⁵×C₅	C₂×C₅×C₉	1	63	yes	—
29	C₂×C₃×C₂₅	C₂⁵×C₃	1	63	yes	—
30	C₂⁴×C₉	C₂²×C₂₅	1	651	yes	direct product factor
31	C₂³×C₃×C₅	C₂³×C₃×C₅	1	1395	yes	—
32	C₂²×C₂₅	C₂⁴×C₉	1	651	yes	direct product factor
33	C₂⁵×C₃	C₂×C₃×C₂₅	1	63	yes	—
34	C₂×C₅×C₉	C₂⁵×C₅	1	63	yes	—
35	C₂⁴×C₅	C₂²×C₅×C₉	1	651	yes	—
36	C₃×C₂₅	C₂⁶×C₃	1	1	yes	characteristic
37	C₂³×C₉	C₂³×C₂₅	1	1395	yes	direct product factor
38	C₂⁶	C₉×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₃×C₅	C₂⁴×C₃×C₅	1	651	yes	—
40	C₂×C₂₅	C₂⁵×C₉	1	63	yes	direct product factor
41	C₂⁴×C₃	C₂²×C₃×C₂₅	1	651	yes	—
42	C₅×C₉	C₂⁶×C₅	1	1	yes	characteristic
43	C₂³×C₅	C₂³×C₅×C₉	1	1395	yes	—
44	C₂²×C₉	C₂⁴×C₂₅	1	651	yes	direct product factor
45	C₂⁵	C₂×C₉×C₂₅	1	63	yes	direct product factor
46	C₂×C₃×C₅	C₂⁵×C₃×C₅	1	63	yes	—
47	C₂₅	C₂⁶×C₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂³×C₃	C₂³×C₃×C₂₅	1	1395	yes	—
49	C₂²×C₅	C₂⁴×C₅×C₉	1	651	yes	—
50	C₂×C₉	C₂⁵×C₂₅	1	63	yes	direct product factor
51	C₂⁴	C₂²×C₉×C₂₅	1	651	yes	direct product factor
52	C₃×C₅	C₂⁶×C₃×C₅	1	1	yes	characteristic
53	C₂²×C₃	C₂⁴×C₃×C₂₅	1	651	yes	—
54	C₂×C₅	C₂⁵×C₅×C₉	1	63	yes	—
55	C₉	C₂⁶×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
56	C₂³	C₂³×C₉×C₂₅	1	1395	yes	direct product factor
57	C₂×C₃	C₂⁵×C₃×C₂₅	1	63	yes	—
58	C₅	C₂⁶×C₅×C₉	1	1	yes	characteristic
59	C₂²	C₂⁴×C₉×C₂₅	1	651	yes	direct product factor
60	C₃	C₂⁶×C₃×C₂₅	1	1	yes	characteristic
61	C₂	C₂⁵×C₉×C₂₅	1	63	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₅	C₂⁶×C₃×C₅
socle, prime radical	C₂⁶×C₃×C₅	C₃×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₉×C₂₅	C₂	direct (N × H)
3. C₂⁴×C₉×C₂₅	C₂²	direct (N × H)
6. C₂³×C₉×C₂₅	C₂³	direct (N × H)
7. C₂⁶×C₂₅	C₉	direct (N × H)
11. C₂²×C₉×C₂₅	C₂⁴	direct (N × H)
12. C₂⁵×C₂₅	C₂×C₉	direct (N × H)
15. C₂⁶×C₉	C₂₅	direct (N × H)
17. C₂×C₉×C₂₅	C₂⁵	direct (N × H)
18. C₂⁴×C₂₅	C₂²×C₉	direct (N × H)
22. C₂⁵×C₉	C₂×C₂₅	direct (N × H)
24. C₉×C₂₅	C₂⁶	direct (N × H)
25. C₂³×C₂₅	C₂³×C₉	direct (N × H)
30. C₂⁴×C₉	C₂²×C₂₅	direct (N × H)
32. C₂²×C₂₅	C₂⁴×C₉	direct (N × H)
37. C₂³×C₉	C₂³×C₂₅	direct (N × H)
38. C₂⁶	C₉×C₂₅	direct (N × H)
40. C₂×C₂₅	C₂⁵×C₉	direct (N × H)
44. C₂²×C₉	C₂⁴×C₂₅	direct (N × H)
45. C₂⁵	C₂×C₉×C₂₅	direct (N × H)
47. C₂₅	C₂⁶×C₉	direct (N × H)
50. C₂×C₉	C₂⁵×C₂₅	direct (N × H)
51. C₂⁴	C₂²×C₉×C₂₅	direct (N × H)
55. C₉	C₂⁶×C₂₅	direct (N × H)
56. C₂³	C₂³×C₉×C₂₅	direct (N × H)
59. C₂²	C₂⁴×C₉×C₂₅	direct (N × H)
61. C₂	C₂⁵×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
C₂⁵×C₉×C₂₅	2
C₂⁶×C₃×C₂₅	3
C₂⁶×C₅×C₉	5

Subgroups — C26×C9×C25 #72192579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×C₉×C₂₅ #72192579