Subgroups — C₂²×C₃×C₉×C₁₃² #72196014

Order 18252.

800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₁₃²	C₂	1	3	yes	maximal, direct product factor
2	C₃×C₉×C₁₃²	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₃²×C₁₃²	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₉×C₁₃²	C₃	1	3	yes	maximal, direct product factor
5	C₂×C₃²×C₁₃²	C₂×C₃	1	3	yes	—
6	C₂×C₉×C₁₃²	C₂×C₃	1	9	yes	direct product factor
7	C₂²×C₃×C₁₃²	C₉	1	3	yes	direct product factor
8	C₂²×C₃×C₁₃²	C₃²	1	1	yes	characteristic
9	C₃²×C₁₃²	C₂²×C₃	1	1	yes	characteristic
10	C₉×C₁₃²	C₂²×C₃	1	3	yes	direct product factor
11	C₂²×C₃×C₉×C₁₃	C₁₃	1	14	yes	maximal, direct product factor
12	C₂×C₃×C₁₃²	C₂×C₉	1	9	yes	direct product factor
13	C₂×C₃×C₁₃²	C₂×C₃²	1	3	yes	—
14	C₂×C₃×C₉×C₁₃	C₂×C₁₃	1	42	yes	direct product factor
15	C₂²×C₁₃²	C₃×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₁₃²	C₂²×C₉	1	3	yes	direct product factor
17	C₃×C₁₃²	C₂²×C₃²	1	1	yes	characteristic
18	C₂²×C₃²×C₁₃	C₃×C₁₃	1	14	yes	—
19	C₂²×C₉×C₁₃	C₃×C₁₃	1	42	yes	direct product factor
20	C₃×C₉×C₁₃	C₂²×C₁₃	1	14	yes	direct product factor
21	C₂×C₁₃²	C₂×C₃×C₉	1	3	yes	direct product factor
22	C₂×C₃²×C₁₃	C₂×C₃×C₁₃	1	42	yes	—
23	C₂×C₉×C₁₃	C₂×C₃×C₁₃	1	126	yes	direct product factor
24	C₁₃²	C₂²×C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²×C₃×C₁₃	C₉×C₁₃	1	42	yes	direct product factor
26	C₂²×C₃×C₁₃	C₃²×C₁₃	1	14	yes	—
27	C₃²×C₁₃	C₂²×C₃×C₁₃	1	14	yes	—
28	C₉×C₁₃	C₂²×C₃×C₁₃	1	42	yes	direct product factor
29	C₂²×C₃×C₉	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₃	C₂×C₉×C₁₃	1	126	yes	direct product factor
31	C₂×C₃×C₁₃	C₂×C₃²×C₁₃	1	42	yes	—
32	C₂×C₃×C₉	C₂×C₁₃²	1	3	yes	direct product factor
33	C₂²×C₁₃	C₃×C₉×C₁₃	1	14	yes	direct product factor
34	C₃×C₁₃	C₂²×C₉×C₁₃	1	42	yes	direct product factor
35	C₃×C₁₃	C₂²×C₃²×C₁₃	1	14	yes	—
36	C₂²×C₃²	C₃×C₁₃²	1	1	yes	characteristic
37	C₂²×C₉	C₃×C₁₃²	1	3	yes	direct product factor
38	C₃×C₉	C₂²×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₁₃	C₂×C₃×C₉×C₁₃	1	42	yes	direct product factor
40	C₂×C₃²	C₂×C₃×C₁₃²	1	3	yes	—
41	C₂×C₉	C₂×C₃×C₁₃²	1	9	yes	direct product factor
42	C₁₃	C₂²×C₃×C₉×C₁₃	1	14	yes	direct product factor
43	C₂²×C₃	C₉×C₁₃²	1	3	yes	direct product factor
44	C₂²×C₃	C₃²×C₁₃²	1	1	yes	characteristic
45	C₃²	C₂²×C₃×C₁₃²	1	1	yes	characteristic
46	C₉	C₂²×C₃×C₁₃²	1	3	yes	direct product factor
47	C₂×C₃	C₂×C₉×C₁₃²	1	9	yes	direct product factor
48	C₂×C₃	C₂×C₃²×C₁₃²	1	3	yes	—
49	C₂²	C₃×C₉×C₁₃²	1	1	yes	characteristic, direct product factor, Sylow
50	C₃	C₂²×C₉×C₁₃²	1	3	yes	direct product factor
51	C₃	C₂²×C₃²×C₁₃²	1	1	yes	characteristic
52	C₂	C₂×C₃×C₉×C₁₃²	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃²×C₁₃²
socle, prime radical	C₂²×C₃²×C₁₃²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×C₁₃²	C₂	direct (N × H)
2. C₃×C₉×C₁₃²	C₂²	direct (N × H)
4. C₂²×C₉×C₁₃²	C₃	direct (N × H)
6. C₂×C₉×C₁₃²	C₂×C₃	direct (N × H)
7. C₂²×C₃×C₁₃²	C₉	direct (N × H)
10. C₉×C₁₃²	C₂²×C₃	direct (N × H)
11. C₂²×C₃×C₉×C₁₃	C₁₃	direct (N × H)
12. C₂×C₃×C₁₃²	C₂×C₉	direct (N × H)
14. C₂×C₃×C₉×C₁₃	C₂×C₁₃	direct (N × H)
15. C₂²×C₁₃²	C₃×C₉	direct (N × H)
16. C₃×C₁₃²	C₂²×C₉	direct (N × H)
19. C₂²×C₉×C₁₃	C₃×C₁₃	direct (N × H)
20. C₃×C₉×C₁₃	C₂²×C₁₃	direct (N × H)
21. C₂×C₁₃²	C₂×C₃×C₉	direct (N × H)
23. C₂×C₉×C₁₃	C₂×C₃×C₁₃	direct (N × H)
24. C₁₃²	C₂²×C₃×C₉	direct (N × H)
25. C₂²×C₃×C₁₃	C₉×C₁₃	direct (N × H)
28. C₉×C₁₃	C₂²×C₃×C₁₃	direct (N × H)
29. C₂²×C₃×C₉	C₁₃²	direct (N × H)
30. C₂×C₃×C₁₃	C₂×C₉×C₁₃	direct (N × H)
32. C₂×C₃×C₉	C₂×C₁₃²	direct (N × H)
33. C₂²×C₁₃	C₃×C₉×C₁₃	direct (N × H)
34. C₃×C₁₃	C₂²×C₉×C₁₃	direct (N × H)
37. C₂²×C₉	C₃×C₁₃²	direct (N × H)
38. C₃×C₉	C₂²×C₁₃²	direct (N × H)
39. C₂×C₁₃	C₂×C₃×C₉×C₁₃	direct (N × H)
41. C₂×C₉	C₂×C₃×C₁₃²	direct (N × H)
42. C₁₃	C₂²×C₃×C₉×C₁₃	direct (N × H)
43. C₂²×C₃	C₉×C₁₃²	direct (N × H)
46. C₉	C₂²×C₃×C₁₃²	direct (N × H)
47. C₂×C₃	C₂×C₉×C₁₃²	direct (N × H)
49. C₂²	C₃×C₉×C₁₃²	direct (N × H)
50. C₃	C₂²×C₉×C₁₃²	direct (N × H)
52. C₂	C₂×C₃×C₉×C₁₃²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×C₁₃²	2
C₂²×C₃²×C₁₃²	3
C₂²×C₉×C₁₃²	3
C₂²×C₃×C₉×C₁₃	13

Subgroups — C22×C3×C9×C132 #72196014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₉×C₁₃² #72196014