Subgroups — C₃×C₅×C₈×C₁₁×C₁₇ #72199842

Order 22440.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₁₁×C₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₈×C₁₁×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₈×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₅×C₁₁×C₁₇	C₄	1	1	yes	characteristic
6	C₄×C₅×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅×C₁₁×C₁₇	C₈	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₄×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic
9	C₂×C₅×C₁₁×C₁₇	C₃×C₄	1	1	yes	characteristic
10	C₈×C₁₁×C₁₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅×C₈×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₁₁×C₁₇	C₄×C₅	1	1	yes	characteristic
13	C₃×C₄×C₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic
14	C₅×C₁₁×C₁₇	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
16	C₅×C₈×C₁₇	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₄×C₅×C₁₁	C₂×C₁₇	1	1	yes	characteristic
18	C₃×C₁₁×C₁₇	C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₅×C₁₇	C₄×C₁₁	1	1	yes	characteristic
20	C₅×C₈×C₁₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₈×C₁₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₁×C₁₇	C₃×C₄×C₅	1	1	yes	characteristic
23	C₄×C₅×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic
24	C₂×C₃×C₅×C₁₁	C₄×C₁₇	1	1	yes	characteristic
25	C₃×C₈×C₁₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₁₇	C₈×C₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₄×C₅×C₁₁	C₂×C₃×C₁₇	1	1	yes	characteristic
28	C₃×C₄×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic
29	C₁₁×C₁₇	C₃×C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₅×C₁₇	C₃×C₄×C₁₁	1	1	yes	characteristic
31	C₃×C₅×C₁₁	C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
32	C₈×C₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
33	C₃×C₄×C₁₁	C₂×C₅×C₁₇	1	1	yes	characteristic
34	C₃×C₅×C₈	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₅×C₁₁	C₃×C₄×C₁₇	1	1	yes	characteristic
36	C₂×C₃×C₁₇	C₄×C₅×C₁₁	1	1	yes	characteristic
37	C₈×C₁₁	C₃×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
38	C₅×C₁₇	C₃×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Hall
39	C₄×C₁₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
40	C₂×C₃×C₁₁	C₄×C₅×C₁₇	1	1	yes	characteristic
41	C₃×C₄×C₅	C₂×C₁₁×C₁₇	1	1	yes	characteristic
42	C₅×C₁₁	C₃×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
43	C₃×C₁₇	C₅×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Hall
44	C₄×C₁₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
45	C₅×C₈	C₃×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
46	C₂×C₁₇	C₃×C₄×C₅×C₁₁	1	1	yes	characteristic
47	C₃×C₁₁	C₅×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₃×C₅	C₄×C₁₁×C₁₇	1	1	yes	characteristic
49	C₃×C₈	C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
50	C₂×C₁₁	C₃×C₄×C₅×C₁₇	1	1	yes	characteristic
51	C₄×C₅	C₂×C₃×C₁₁×C₁₇	1	1	yes	characteristic
52	C₁₇	C₃×C₅×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
53	C₃×C₅	C₈×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
54	C₃×C₄	C₂×C₅×C₁₁×C₁₇	1	1	yes	characteristic
55	C₁₁	C₃×C₅×C₈×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×C₅	C₃×C₄×C₁₁×C₁₇	1	1	yes	characteristic
57	C₈	C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
58	C₂×C₃	C₄×C₅×C₁₁×C₁₇	1	1	yes	characteristic
59	C₅	C₃×C₈×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
60	C₄	C₂×C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic
61	C₃	C₅×C₈×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	C₃×C₄×C₅×C₁₁×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅×C₁₁×C₁₇
socle, prime radical	C₂×C₃×C₅×C₁₁×C₁₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₈×C₁₁×C₁₇	C₃	direct (N × H)
2. C₃×C₈×C₁₁×C₁₇	C₅	direct (N × H)
3. C₃×C₅×C₈×C₁₇	C₁₁	direct (N × H)
7. C₃×C₅×C₁₁×C₁₇	C₈	direct (N × H)
10. C₈×C₁₁×C₁₇	C₃×C₅	direct (N × H)
11. C₃×C₅×C₈×C₁₁	C₁₇	direct (N × H)
14. C₅×C₁₁×C₁₇	C₃×C₈	direct (N × H)
16. C₅×C₈×C₁₇	C₃×C₁₁	direct (N × H)
18. C₃×C₁₁×C₁₇	C₅×C₈	direct (N × H)
20. C₅×C₈×C₁₁	C₃×C₁₇	direct (N × H)
21. C₃×C₈×C₁₇	C₅×C₁₁	direct (N × H)
25. C₃×C₈×C₁₁	C₅×C₁₇	direct (N × H)
26. C₃×C₅×C₁₇	C₈×C₁₁	direct (N × H)
29. C₁₁×C₁₇	C₃×C₅×C₈	direct (N × H)
31. C₃×C₅×C₁₁	C₈×C₁₇	direct (N × H)
32. C₈×C₁₇	C₃×C₅×C₁₁	direct (N × H)
34. C₃×C₅×C₈	C₁₁×C₁₇	direct (N × H)
37. C₈×C₁₁	C₃×C₅×C₁₇	direct (N × H)
38. C₅×C₁₇	C₃×C₈×C₁₁	direct (N × H)
42. C₅×C₁₁	C₃×C₈×C₁₇	direct (N × H)
43. C₃×C₁₇	C₅×C₈×C₁₁	direct (N × H)
45. C₅×C₈	C₃×C₁₁×C₁₇	direct (N × H)
47. C₃×C₁₁	C₅×C₈×C₁₇	direct (N × H)
49. C₃×C₈	C₅×C₁₁×C₁₇	direct (N × H)
52. C₁₇	C₃×C₅×C₈×C₁₁	direct (N × H)
53. C₃×C₅	C₈×C₁₁×C₁₇	direct (N × H)
55. C₁₁	C₃×C₅×C₈×C₁₇	direct (N × H)
57. C₈	C₃×C₅×C₁₁×C₁₇	direct (N × H)
59. C₅	C₃×C₈×C₁₁×C₁₇	direct (N × H)
61. C₃	C₅×C₈×C₁₁×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×C₁₁×C₁₇	3
C₃×C₈×C₁₁×C₁₇	5
C₃×C₅×C₈×C₁₇	11
C₃×C₄×C₅×C₁₁×C₁₇	2
C₃×C₅×C₈×C₁₁	17

Subgroups — C3×C5×C8×C11×C17 #72199842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₈×C₁₁×C₁₇ #72199842