Subgroups — C₂×C₃×C₈×C₁₇×C₂₉ #72201010

Order 23664.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₁₇×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×C₁₇×C₂₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₈×C₁₇×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₄×C₁₇×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₈×C₁₇×C₂₉	C₂×C₃	1	2	yes	direct product factor
6	C₂²×C₃×C₁₇×C₂₉	C₄	1	1	yes	characteristic
7	C₃×C₄×C₁₇×C₂₉	C₄	1	1	yes	characteristic
8	C₃×C₄×C₁₇×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₁₇×C₂₉	C₈	1	2	yes	direct product factor
10	C₂×C₃×C₁₇×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₇×C₂₉	C₃×C₄	1	1	yes	characteristic
12	C₄×C₁₇×C₂₉	C₃×C₄	1	1	yes	characteristic
13	C₄×C₁₇×C₂₉	C₂²×C₃	1	1	yes	characteristic
14	C₃×C₁₇×C₂₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₈×C₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₇×C₂₉	C₃×C₈	1	2	yes	direct product factor
17	C₂×C₁₇×C₂₉	C₂×C₃×C₄	1	1	yes	characteristic
18	C₂×C₃×C₈×C₁₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₄×C₂₉	C₂×C₁₇	1	1	yes	characteristic
20	C₃×C₈×C₂₉	C₂×C₁₇	1	2	yes	direct product factor
21	C₁₇×C₂₉	C₂×C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₈×C₂₉	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₄×C₁₇	C₂×C₂₉	1	1	yes	characteristic
24	C₃×C₈×C₁₇	C₂×C₂₉	1	2	yes	direct product factor
25	C₂²×C₃×C₂₉	C₄×C₁₇	1	1	yes	characteristic
26	C₃×C₄×C₂₉	C₄×C₁₇	1	1	yes	characteristic
27	C₃×C₄×C₂₉	C₂²×C₁₇	1	1	yes	characteristic
28	C₂×C₈×C₁₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₄×C₂₉	C₂×C₃×C₁₇	1	1	yes	characteristic
30	C₈×C₂₉	C₂×C₃×C₁₇	1	2	yes	direct product factor
31	C₂²×C₃×C₁₇	C₄×C₂₉	1	1	yes	characteristic
32	C₃×C₄×C₁₇	C₄×C₂₉	1	1	yes	characteristic
33	C₃×C₄×C₁₇	C₂²×C₂₉	1	1	yes	characteristic
34	C₂×C₃×C₂₉	C₈×C₁₇	1	2	yes	direct product factor
35	C₂×C₃×C₂₉	C₂×C₄×C₁₇	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×C₃×C₂₉	1	1	yes	characteristic
37	C₈×C₁₇	C₂×C₃×C₂₉	1	2	yes	direct product factor
38	C₂²×C₂₉	C₃×C₄×C₁₇	1	1	yes	characteristic
39	C₄×C₂₉	C₃×C₄×C₁₇	1	1	yes	characteristic
40	C₄×C₂₉	C₂²×C₃×C₁₇	1	1	yes	characteristic
41	C₂×C₃×C₁₇	C₈×C₂₉	1	2	yes	direct product factor
42	C₂×C₃×C₁₇	C₂×C₄×C₂₉	1	1	yes	characteristic
43	C₃×C₂₉	C₂×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₁₇	C₃×C₄×C₂₉	1	1	yes	characteristic
45	C₄×C₁₇	C₃×C₄×C₂₉	1	1	yes	characteristic
46	C₄×C₁₇	C₂²×C₃×C₂₉	1	1	yes	characteristic
47	C₂×C₂₉	C₃×C₈×C₁₇	1	2	yes	direct product factor
48	C₂×C₂₉	C₂×C₃×C₄×C₁₇	1	1	yes	characteristic
49	C₃×C₁₇	C₂×C₈×C₂₉	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₃×C₈	C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₁₇	C₃×C₈×C₂₉	1	2	yes	direct product factor
52	C₂×C₁₇	C₂×C₃×C₄×C₂₉	1	1	yes	characteristic
53	C₂₉	C₂×C₃×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃×C₄	C₂×C₁₇×C₂₉	1	1	yes	characteristic
55	C₃×C₈	C₂×C₁₇×C₂₉	1	2	yes	direct product factor
56	C₁₇	C₂×C₃×C₈×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₈	C₃×C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₃	C₄×C₁₇×C₂₉	1	1	yes	characteristic
59	C₃×C₄	C₄×C₁₇×C₂₉	1	1	yes	characteristic
60	C₃×C₄	C₂²×C₁₇×C₂₉	1	1	yes	characteristic
61	C₂×C₄	C₂×C₃×C₁₇×C₂₉	1	1	yes	characteristic
62	C₈	C₂×C₃×C₁₇×C₂₉	1	2	yes	direct product factor
63	C₂×C₃	C₈×C₁₇×C₂₉	1	2	yes	direct product factor
64	C₂×C₃	C₂×C₄×C₁₇×C₂₉	1	1	yes	characteristic
65	C₂²	C₃×C₄×C₁₇×C₂₉	1	1	yes	characteristic
66	C₄	C₃×C₄×C₁₇×C₂₉	1	1	yes	characteristic
67	C₄	C₂²×C₃×C₁₇×C₂₉	1	1	yes	characteristic
68	C₃	C₂×C₈×C₁₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	C₃×C₈×C₁₇×C₂₉	1	2	yes	direct product factor
70	C₂	C₂×C₃×C₄×C₁₇×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃×C₁₇×C₂₉
socle, prime radical	C₂²×C₃×C₁₇×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. C₃×C₈×C₁₇×C₂₉	C₂	direct (N × H)
3. C₂×C₈×C₁₇×C₂₉	C₃	direct (N × H)
5. C₈×C₁₇×C₂₉	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₇×C₂₉	C₈	direct (N × H)
14. C₃×C₁₇×C₂₉	C₂×C₈	direct (N × H)
15. C₂×C₃×C₈×C₂₉	C₁₇	direct (N × H)
16. C₂×C₁₇×C₂₉	C₃×C₈	direct (N × H)
18. C₂×C₃×C₈×C₁₇	C₂₉	direct (N × H)
20. C₃×C₈×C₂₉	C₂×C₁₇	direct (N × H)
21. C₁₇×C₂₉	C₂×C₃×C₈	direct (N × H)
22. C₂×C₈×C₂₉	C₃×C₁₇	direct (N × H)
24. C₃×C₈×C₁₇	C₂×C₂₉	direct (N × H)
28. C₂×C₈×C₁₇	C₃×C₂₉	direct (N × H)
30. C₈×C₂₉	C₂×C₃×C₁₇	direct (N × H)
34. C₂×C₃×C₂₉	C₈×C₁₇	direct (N × H)
37. C₈×C₁₇	C₂×C₃×C₂₉	direct (N × H)
41. C₂×C₃×C₁₇	C₈×C₂₉	direct (N × H)
43. C₃×C₂₉	C₂×C₈×C₁₇	direct (N × H)
47. C₂×C₂₉	C₃×C₈×C₁₇	direct (N × H)
49. C₃×C₁₇	C₂×C₈×C₂₉	direct (N × H)
50. C₂×C₃×C₈	C₁₇×C₂₉	direct (N × H)
51. C₂×C₁₇	C₃×C₈×C₂₉	direct (N × H)
53. C₂₉	C₂×C₃×C₈×C₁₇	direct (N × H)
55. C₃×C₈	C₂×C₁₇×C₂₉	direct (N × H)
56. C₁₇	C₂×C₃×C₈×C₂₉	direct (N × H)
57. C₂×C₈	C₃×C₁₇×C₂₉	direct (N × H)
62. C₈	C₂×C₃×C₁₇×C₂₉	direct (N × H)
63. C₂×C₃	C₈×C₁₇×C₂₉	direct (N × H)
68. C₃	C₂×C₈×C₁₇×C₂₉	direct (N × H)
69. C₂	C₃×C₈×C₁₇×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×C₃×C₄×C₁₇×C₂₉	2
C₃×C₈×C₁₇×C₂₉	2
C₂×C₈×C₁₇×C₂₉	3
C₂×C₃×C₈×C₂₉	17
C₂×C₃×C₈×C₁₇	29

Subgroups — C2×C3×C8×C17×C29 #72201010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₈×C₁₇×C₂₉ #72201010