Subgroups — C₂×C₃³×C₈×C₂₉ #72190871

Order 12528.

616 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₈×C₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₈×C₂₉	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³×C₂₉	C₄	1	1	yes	characteristic
5	C₃³×C₄×C₂₉	C₄	1	1	yes	characteristic
6	C₃³×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄×C₂₉	C₂×C₃	1	13	yes	—
8	C₃²×C₈×C₂₉	C₂×C₃	1	26	yes	direct product factor
9	C₂×C₃³×C₂₉	C₈	1	2	yes	direct product factor
10	C₂×C₃³×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₈×C₂₉	C₃²	1	13	yes	direct product factor
12	C₂²×C₃²×C₂₉	C₃×C₄	1	13	yes	—
13	C₃²×C₄×C₂₉	C₃×C₄	1	13	yes	—
14	C₃²×C₄×C₂₉	C₂²×C₃	1	13	yes	—
15	C₃³×C₂₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₄×C₂₉	C₂×C₃²	1	13	yes	—
17	C₃×C₈×C₂₉	C₂×C₃²	1	26	yes	direct product factor
18	C₂×C₃²×C₂₉	C₃×C₈	1	26	yes	direct product factor
19	C₂×C₃²×C₂₉	C₂×C₃×C₄	1	13	yes	—
20	C₂×C₈×C₂₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃³×C₈	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂²×C₃×C₂₉	C₃²×C₄	1	13	yes	—
23	C₃×C₄×C₂₉	C₃²×C₄	1	13	yes	—
24	C₃×C₄×C₂₉	C₂²×C₃²	1	13	yes	—
25	C₃²×C₂₉	C₂×C₃×C₈	1	13	yes	direct product factor
26	C₂×C₄×C₂₉	C₂×C₃³	1	1	yes	characteristic
27	C₈×C₂₉	C₂×C₃³	1	2	yes	direct product factor
28	C₂×C₃³×C₄	C₂×C₂₉	1	1	yes	characteristic
29	C₃³×C₈	C₂×C₂₉	1	2	yes	direct product factor
30	C₂×C₃×C₂₉	C₃²×C₈	1	26	yes	direct product factor
31	C₂×C₃×C₂₉	C₂×C₃²×C₄	1	13	yes	—
32	C₂×C₃²×C₈	C₃×C₂₉	1	13	yes	direct product factor
33	C₂²×C₂₉	C₃³×C₄	1	1	yes	characteristic
34	C₄×C₂₉	C₃³×C₄	1	1	yes	characteristic
35	C₄×C₂₉	C₂²×C₃³	1	1	yes	characteristic
36	C₂²×C₃³	C₄×C₂₉	1	1	yes	characteristic
37	C₃³×C₄	C₄×C₂₉	1	1	yes	characteristic
38	C₃³×C₄	C₂²×C₂₉	1	1	yes	characteristic
39	C₃×C₂₉	C₂×C₃²×C₈	1	13	yes	direct product factor
40	C₂×C₃²×C₄	C₂×C₃×C₂₉	1	13	yes	—
41	C₃²×C₈	C₂×C₃×C₂₉	1	26	yes	direct product factor
42	C₂×C₂₉	C₃³×C₈	1	2	yes	direct product factor
43	C₂×C₂₉	C₂×C₃³×C₄	1	1	yes	characteristic
44	C₂×C₃³	C₈×C₂₉	1	2	yes	direct product factor
45	C₂×C₃³	C₂×C₄×C₂₉	1	1	yes	characteristic
46	C₂×C₃×C₈	C₃²×C₂₉	1	13	yes	direct product factor
47	C₂²×C₃²	C₃×C₄×C₂₉	1	13	yes	—
48	C₃²×C₄	C₃×C₄×C₂₉	1	13	yes	—
49	C₃²×C₄	C₂²×C₃×C₂₉	1	13	yes	—
50	C₂₉	C₂×C₃³×C₈	1	1	yes	characteristic, direct product factor, Sylow
51	C₃³	C₂×C₈×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₃×C₄	C₂×C₃²×C₂₉	1	13	yes	—
53	C₃×C₈	C₂×C₃²×C₂₉	1	26	yes	direct product factor
54	C₂×C₃²	C₃×C₈×C₂₉	1	26	yes	direct product factor
55	C₂×C₃²	C₂×C₃×C₄×C₂₉	1	13	yes	—
56	C₂×C₈	C₃³×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	C₃²×C₄×C₂₉	1	13	yes	—
58	C₃×C₄	C₃²×C₄×C₂₉	1	13	yes	—
59	C₃×C₄	C₂²×C₃²×C₂₉	1	13	yes	—
60	C₃²	C₂×C₃×C₈×C₂₉	1	13	yes	direct product factor
61	C₂×C₄	C₂×C₃³×C₂₉	1	1	yes	characteristic
62	C₈	C₂×C₃³×C₂₉	1	2	yes	direct product factor
63	C₂×C₃	C₃²×C₈×C₂₉	1	26	yes	direct product factor
64	C₂×C₃	C₂×C₃²×C₄×C₂₉	1	13	yes	—
65	C₂²	C₃³×C₄×C₂₉	1	1	yes	characteristic
66	C₄	C₃³×C₄×C₂₉	1	1	yes	characteristic
67	C₄	C₂²×C₃³×C₂₉	1	1	yes	characteristic
68	C₃	C₂×C₃²×C₈×C₂₉	1	13	yes	direct product factor
69	C₂	C₃³×C₈×C₂₉	1	2	yes	direct product factor
70	C₂	C₂×C₃³×C₄×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃³×C₂₉
socle, prime radical	C₂²×C₃³×C₂₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₈×C₂₉	C₂	direct (N × H)
3. C₂×C₃²×C₈×C₂₉	C₃	direct (N × H)
8. C₃²×C₈×C₂₉	C₂×C₃	direct (N × H)
9. C₂×C₃³×C₂₉	C₈	direct (N × H)
11. C₂×C₃×C₈×C₂₉	C₃²	direct (N × H)
15. C₃³×C₂₉	C₂×C₈	direct (N × H)
17. C₃×C₈×C₂₉	C₂×C₃²	direct (N × H)
18. C₂×C₃²×C₂₉	C₃×C₈	direct (N × H)
20. C₂×C₈×C₂₉	C₃³	direct (N × H)
21. C₂×C₃³×C₈	C₂₉	direct (N × H)
25. C₃²×C₂₉	C₂×C₃×C₈	direct (N × H)
27. C₈×C₂₉	C₂×C₃³	direct (N × H)
29. C₃³×C₈	C₂×C₂₉	direct (N × H)
30. C₂×C₃×C₂₉	C₃²×C₈	direct (N × H)
32. C₂×C₃²×C₈	C₃×C₂₉	direct (N × H)
39. C₃×C₂₉	C₂×C₃²×C₈	direct (N × H)
41. C₃²×C₈	C₂×C₃×C₂₉	direct (N × H)
42. C₂×C₂₉	C₃³×C₈	direct (N × H)
44. C₂×C₃³	C₈×C₂₉	direct (N × H)
46. C₂×C₃×C₈	C₃²×C₂₉	direct (N × H)
50. C₂₉	C₂×C₃³×C₈	direct (N × H)
51. C₃³	C₂×C₈×C₂₉	direct (N × H)
53. C₃×C₈	C₂×C₃²×C₂₉	direct (N × H)
54. C₂×C₃²	C₃×C₈×C₂₉	direct (N × H)
56. C₂×C₈	C₃³×C₂₉	direct (N × H)
60. C₃²	C₂×C₃×C₈×C₂₉	direct (N × H)
62. C₈	C₂×C₃³×C₂₉	direct (N × H)
63. C₂×C₃	C₃²×C₈×C₂₉	direct (N × H)
68. C₃	C₂×C₃²×C₈×C₂₉	direct (N × H)
69. C₂	C₃³×C₈×C₂₉	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×C₃³×C₄×C₂₉	2
C₃³×C₈×C₂₉	2
C₂×C₃²×C₈×C₂₉	3
C₂×C₃³×C₈	29

Subgroups — C2×C33×C8×C29 #72190871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₈×C₂₉ #72190871