Subgroups — C₂×C₄×C₅×C₁₇×C₄₇ #72208682

Order 31960.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₇×C₄₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂²×C₅×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₁₇×C₄₇	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₅×C₁₇×C₄₇	C₄	1	2	yes	direct product factor
5	C₂×C₅×C₁₇×C₄₇	C₂²	1	1	yes	characteristic
6	C₅×C₁₇×C₄₇	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
7	C₂²×C₁₇×C₄₇	C₂×C₅	1	1	yes	characteristic
8	C₄×C₁₇×C₄₇	C₂×C₅	1	2	yes	direct product factor
9	C₂×C₄×C₅×C₄₇	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₇×C₄₇	C₄×C₅	1	2	yes	direct product factor
11	C₂×C₁₇×C₄₇	C₂²×C₅	1	1	yes	characteristic
12	C₂²×C₅×C₄₇	C₂×C₁₇	1	1	yes	characteristic
13	C₄×C₅×C₄₇	C₂×C₁₇	1	2	yes	direct product factor
14	C₁₇×C₄₇	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₄×C₅×C₁₇	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×C₄₇	C₄×C₁₇	1	2	yes	direct product factor
17	C₂×C₅×C₄₇	C₂²×C₁₇	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₅×C₁₇	C₂×C₄₇	1	1	yes	characteristic
20	C₄×C₅×C₁₇	C₂×C₄₇	1	2	yes	direct product factor
21	C₅×C₄₇	C₂×C₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₄₇	C₂×C₅×C₁₇	1	1	yes	characteristic
23	C₄×C₄₇	C₂×C₅×C₁₇	1	2	yes	direct product factor
24	C₂×C₅×C₁₇	C₄×C₄₇	1	2	yes	direct product factor
25	C₂×C₅×C₁₇	C₂²×C₄₇	1	1	yes	characteristic
26	C₂×C₄×C₁₇	C₅×C₄₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₄₇	C₄×C₅×C₁₇	1	2	yes	direct product factor
28	C₂×C₄₇	C₂²×C₅×C₁₇	1	1	yes	characteristic
29	C₅×C₁₇	C₂×C₄×C₄₇	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₁₇	C₂×C₅×C₄₇	1	1	yes	characteristic
31	C₄×C₁₇	C₂×C₅×C₄₇	1	2	yes	direct product factor
32	C₄₇	C₂×C₄×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₄×C₅	C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₇	C₄×C₅×C₄₇	1	2	yes	direct product factor
35	C₂×C₁₇	C₂²×C₅×C₄₇	1	1	yes	characteristic
36	C₂²×C₅	C₂×C₁₇×C₄₇	1	1	yes	characteristic
37	C₄×C₅	C₂×C₁₇×C₄₇	1	2	yes	direct product factor
38	C₁₇	C₂×C₄×C₅×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₅	C₄×C₁₇×C₄₇	1	2	yes	direct product factor
40	C₂×C₅	C₂²×C₁₇×C₄₇	1	1	yes	characteristic
41	C₂×C₄	C₅×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₅	C₂×C₄×C₁₇×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	C₂×C₅×C₁₇×C₄₇	1	1	yes	characteristic
44	C₄	C₂×C₅×C₁₇×C₄₇	1	2	yes	direct product factor
45	C₂	C₄×C₅×C₁₇×C₄₇	1	2	yes	direct product factor
46	C₂	C₂²×C₅×C₁₇×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₁₇×C₄₇
socle, prime radical	C₂²×C₅×C₁₇×C₄₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₁₇×C₄₇	C₅	direct (N × H)
3. C₄×C₅×C₁₇×C₄₇	C₂	direct (N × H)
4. C₂×C₅×C₁₇×C₄₇	C₄	direct (N × H)
6. C₅×C₁₇×C₄₇	C₂×C₄	direct (N × H)
8. C₄×C₁₇×C₄₇	C₂×C₅	direct (N × H)
9. C₂×C₄×C₅×C₄₇	C₁₇	direct (N × H)
10. C₂×C₁₇×C₄₇	C₄×C₅	direct (N × H)
13. C₄×C₅×C₄₇	C₂×C₁₇	direct (N × H)
14. C₁₇×C₄₇	C₂×C₄×C₅	direct (N × H)
15. C₂×C₄×C₅×C₁₇	C₄₇	direct (N × H)
16. C₂×C₅×C₄₇	C₄×C₁₇	direct (N × H)
18. C₂×C₄×C₄₇	C₅×C₁₇	direct (N × H)
20. C₄×C₅×C₁₇	C₂×C₄₇	direct (N × H)
21. C₅×C₄₇	C₂×C₄×C₁₇	direct (N × H)
23. C₄×C₄₇	C₂×C₅×C₁₇	direct (N × H)
24. C₂×C₅×C₁₇	C₄×C₄₇	direct (N × H)
26. C₂×C₄×C₁₇	C₅×C₄₇	direct (N × H)
27. C₂×C₄₇	C₄×C₅×C₁₇	direct (N × H)
29. C₅×C₁₇	C₂×C₄×C₄₇	direct (N × H)
31. C₄×C₁₇	C₂×C₅×C₄₇	direct (N × H)
32. C₄₇	C₂×C₄×C₅×C₁₇	direct (N × H)
33. C₂×C₄×C₅	C₁₇×C₄₇	direct (N × H)
34. C₂×C₁₇	C₄×C₅×C₄₇	direct (N × H)
37. C₄×C₅	C₂×C₁₇×C₄₇	direct (N × H)
38. C₁₇	C₂×C₄×C₅×C₄₇	direct (N × H)
39. C₂×C₅	C₄×C₁₇×C₄₇	direct (N × H)
41. C₂×C₄	C₅×C₁₇×C₄₇	direct (N × H)
42. C₅	C₂×C₄×C₁₇×C₄₇	direct (N × H)
44. C₄	C₂×C₅×C₁₇×C₄₇	direct (N × H)
45. C₂	C₄×C₅×C₁₇×C₄₇	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×C₄×C₁₇×C₄₇	5
C₂²×C₅×C₁₇×C₄₇	2
C₄×C₅×C₁₇×C₄₇	2
C₂×C₄×C₅×C₄₇	17
C₂×C₄×C₅×C₁₇	47

Subgroups — C2×C4×C5×C17×C47 #72208682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₁₇×C₄₇ #72208682