Subgroups — C₃²×C₈×C₉×C₁₃ #72187293

Order 8424.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₈×C₉×C₁₃	C₃	1	12	yes	maximal, direct product factor
4	C₂×C₃²×C₉×C₁₃	C₄	1	1	yes	characteristic
5	C₃³×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×C₉×C₁₃	C₂×C₃	1	12	yes	—
7	C₃²×C₉×C₁₃	C₈	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₈×C₁₃	C₉	1	9	yes	direct product factor
9	C₃²×C₈×C₁₃	C₃²	1	4	yes	—
10	C₈×C₉×C₁₃	C₃²	1	9	yes	direct product factor
11	C₂×C₃³×C₁₃	C₃×C₄	1	1	yes	characteristic
12	C₂×C₃×C₉×C₁₃	C₃×C₄	1	12	yes	—
13	C₃²×C₈×C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃²×C₄×C₁₃	C₂×C₉	1	9	yes	—
15	C₃²×C₄×C₁₃	C₂×C₃²	1	4	yes	—
16	C₄×C₉×C₁₃	C₂×C₃²	1	9	yes	—
17	C₃³×C₁₃	C₃×C₈	1	1	yes	characteristic
18	C₃×C₉×C₁₃	C₃×C₈	1	12	yes	direct product factor
19	C₃²×C₄×C₉	C₂×C₁₃	1	1	yes	characteristic
20	C₃×C₈×C₁₃	C₃×C₉	1	12	yes	direct product factor
21	C₃×C₈×C₁₃	C₃³	1	1	yes	characteristic
22	C₂×C₃²×C₁₃	C₄×C₉	1	9	yes	—
23	C₂×C₃²×C₁₃	C₃²×C₄	1	4	yes	—
24	C₂×C₉×C₁₃	C₃²×C₄	1	9	yes	—
25	C₃³×C₈	C₃×C₁₃	1	1	yes	characteristic
26	C₃×C₈×C₉	C₃×C₁₃	1	12	yes	direct product factor
27	C₂×C₃²×C₉	C₄×C₁₃	1	1	yes	characteristic
28	C₃×C₄×C₁₃	C₂×C₃×C₉	1	12	yes	—
29	C₃×C₄×C₁₃	C₂×C₃³	1	1	yes	characteristic
30	C₃²×C₁₃	C₈×C₉	1	9	yes	direct product factor
31	C₃²×C₁₃	C₃²×C₈	1	4	yes	—
32	C₉×C₁₃	C₃²×C₈	1	9	yes	direct product factor
33	C₃³×C₄	C₂×C₃×C₁₃	1	1	yes	characteristic
34	C₃×C₄×C₉	C₂×C₃×C₁₃	1	12	yes	—
35	C₈×C₁₃	C₃²×C₉	1	1	yes	characteristic, direct product factor, Hall
36	C₃²×C₉	C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃×C₁₃	C₃×C₄×C₉	1	12	yes	—
38	C₂×C₃×C₁₃	C₃³×C₄	1	1	yes	characteristic
39	C₃²×C₈	C₉×C₁₃	1	9	yes	direct product factor
40	C₃²×C₈	C₃²×C₁₃	1	4	yes	—
41	C₈×C₉	C₃²×C₁₃	1	9	yes	direct product factor
42	C₂×C₃³	C₃×C₄×C₁₃	1	1	yes	characteristic
43	C₂×C₃×C₉	C₃×C₄×C₁₃	1	12	yes	—
44	C₄×C₁₃	C₂×C₃²×C₉	1	1	yes	characteristic
45	C₃×C₁₃	C₃×C₈×C₉	1	12	yes	direct product factor
46	C₃×C₁₃	C₃³×C₈	1	1	yes	characteristic
47	C₃²×C₄	C₂×C₉×C₁₃	1	9	yes	—
48	C₃²×C₄	C₂×C₃²×C₁₃	1	4	yes	—
49	C₄×C₉	C₂×C₃²×C₁₃	1	9	yes	—
50	C₃³	C₃×C₈×C₁₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₈×C₁₃	1	12	yes	direct product factor
52	C₂×C₁₃	C₃²×C₄×C₉	1	1	yes	characteristic
53	C₃×C₈	C₃×C₉×C₁₃	1	12	yes	direct product factor
54	C₃×C₈	C₃³×C₁₃	1	1	yes	characteristic
55	C₂×C₃²	C₄×C₉×C₁₃	1	9	yes	—
56	C₂×C₃²	C₃²×C₄×C₁₃	1	4	yes	—
57	C₂×C₉	C₃²×C₄×C₁₃	1	9	yes	—
58	C₁₃	C₃²×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
59	C₃×C₄	C₂×C₃×C₉×C₁₃	1	12	yes	—
60	C₃×C₄	C₂×C₃³×C₁₃	1	1	yes	characteristic
61	C₃²	C₈×C₉×C₁₃	1	9	yes	direct product factor
62	C₃²	C₃²×C₈×C₁₃	1	4	yes	—
63	C₉	C₃²×C₈×C₁₃	1	9	yes	direct product factor
64	C₈	C₃²×C₉×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₃	C₃×C₄×C₉×C₁₃	1	12	yes	—
66	C₂×C₃	C₃³×C₄×C₁₃	1	1	yes	characteristic
67	C₄	C₂×C₃²×C₉×C₁₃	1	1	yes	characteristic
68	C₃	C₃×C₈×C₉×C₁₃	1	12	yes	direct product factor
69	C₃	C₃³×C₈×C₁₃	1	1	yes	characteristic
70	C₂	C₃²×C₄×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃³×C₁₃
socle, prime radical	C₂×C₃³×C₁₃	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₈×C₉×C₁₃	C₃	direct (N × H)
7. C₃²×C₉×C₁₃	C₈	direct (N × H)
8. C₃²×C₈×C₁₃	C₉	direct (N × H)
10. C₈×C₉×C₁₃	C₃²	direct (N × H)
13. C₃²×C₈×C₉	C₁₃	direct (N × H)
18. C₃×C₉×C₁₃	C₃×C₈	direct (N × H)
20. C₃×C₈×C₁₃	C₃×C₉	direct (N × H)
26. C₃×C₈×C₉	C₃×C₁₃	direct (N × H)
30. C₃²×C₁₃	C₈×C₉	direct (N × H)
32. C₉×C₁₃	C₃²×C₈	direct (N × H)
35. C₈×C₁₃	C₃²×C₉	direct (N × H)
36. C₃²×C₉	C₈×C₁₃	direct (N × H)
39. C₃²×C₈	C₉×C₁₃	direct (N × H)
41. C₈×C₉	C₃²×C₁₃	direct (N × H)
45. C₃×C₁₃	C₃×C₈×C₉	direct (N × H)
51. C₃×C₉	C₃×C₈×C₁₃	direct (N × H)
53. C₃×C₈	C₃×C₉×C₁₃	direct (N × H)
58. C₁₃	C₃²×C₈×C₉	direct (N × H)
61. C₃²	C₈×C₉×C₁₃	direct (N × H)
63. C₉	C₃²×C₈×C₁₃	direct (N × H)
64. C₈	C₃²×C₉×C₁₃	direct (N × H)
68. C₃	C₃×C₈×C₉×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₄×C₉×C₁₃	2
C₃³×C₈×C₁₃	3
C₃×C₈×C₉×C₁₃	3
C₃²×C₈×C₉	13

Subgroups — C32×C8×C9×C13 #72187293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₈×C₉×C₁₃ #72187293